Chris has worked throughly with my son on his IB past papers. I am extremely impressed with his professional approach to teaching, his quick response to my messages and his helpfulness in finding a solution with regard to timing, days, etc. He is very knowledgeable about the workings of MyTutorWeb, which put me at ease with the whole process. Thank you Chris! :o)

Sheila, Parent from Genève

Why limit yourself to someone who lives nearby, when you can choose from tutors across the UK?

By removing time spent travelling, you make tuition more convenient, flexible and affordable

We've combined live video with a shared whiteboard, so you can work through problems together

All your tutorials are recorded. Make the most out of your live session, then play it back after

Usually we cover both subject knowledge and exam technique, although that can change depending on each individual student. Then we go through diagrams, and they ask questions, and we go from there.

Lots of students say that the classes are too big in school, or that they don't have time to ask teachers after lessons. In my tutorials, we take time to explore things in a little in a bit more detail.

I always look up the board my students are taking so the lessons are really relevant. Then we go through past papers or set texts, whatever the student finds helpful.

I use the shared whiteboard. We make diagrams together and label them, and often the student prints it off because they know it's right and they completely understand it.

After tutoring one girl went and told all her friends the new explanation I gave her. And she was so excited about what she wrote in the exam she emailed me immediately afterwards.

There was one girl who had her exam on Monday. She wanted tuition on Friday, Saturday and Sunday beforehand. It was very intense, but she said the exam went well.

First solve for the exact point on the line by substituting 5 into the original equation. You should get y=+-4.

Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yield the following: dy/dx=(2x)/(3y). Because we only have one value of x, let's substitute this into the derivative first: dy/dx=10/3y. Now we can individually substitute the two y values to get the two values of dy/dx. dy/dx = 10/12 = 5/6, dy/dx = -10/12 = -5/6 These are the two values of dy/dx when x=5.

Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yield the following: dy/dx=(2x)/(3y). Because we only have one value of x, let's substitute this into the derivative first: dy/dx=10/3y. Now we can individually substitute the two y values to get the two values of dy/dx. dy/dx = 10/12 = 5/6, dy/dx = -10/12 = -5/6 These are the two values of dy/dx when x=5.

Answered by Kalid U.

Studies Theoretical Physics at University College London

Firstly, as with any question, make sure to check your formula book in order to find any relevant equations. In this case, the one most relevant to us is U_{n} = U_{1} + d(n-1).

From here we will need to find the common difference of the sequence, 'd'. You could do this by substituting the information we have into the formula, but a much simpler way would be to take the first term of the sequence away from the second; so 5 - 2 = 3. We can check this by taking the second away from the third, 8 - 5 = 3. Therefore, d = 3.

a) We can now substitute our information into the equation to find U_{101, }

U_{101} = U_{1} + d(n-1)

We know that n = 101, U_{1} is the first term of the sequence, 2, and that d = 3.

So, U_{101} = 2 + 3(101-1)

Solving this gets us to U_{101} = 2 + 3(100), U_{101} = 2 + 300, U_{101} = 302.
b) Here we start by again substituting our given information into the formula.

152 = 2 + 3(n-1)

We can see that in this instance 'n' is the unknown term.

By rearranging our equation we will be able to solve for n.

So, we need our common terms to be on the same side of the equation:

Minus two from both sides gives us 150 = 3(n-1).

Dividing by 3 will then give us 50 = n - 1

Now we just need to add 1 to both sides leaving us with 51 = n.

From here we will need to find the common difference of the sequence, 'd'. You could do this by substituting the information we have into the formula, but a much simpler way would be to take the first term of the sequence away from the second; so 5 - 2 = 3. We can check this by taking the second away from the third, 8 - 5 = 3. Therefore, d = 3.

a) We can now substitute our information into the equation to find U

U

We know that n = 101, U

So, U

Solving this gets us to U

152 = 2 + 3(n-1)

We can see that in this instance 'n' is the unknown term.

By rearranging our equation we will be able to solve for n.

So, we need our common terms to be on the same side of the equation:

Minus two from both sides gives us 150 = 3(n-1).

Dividing by 3 will then give us 50 = n - 1

Now we just need to add 1 to both sides leaving us with 51 = n.

Using the implicit form derivative rule: y'=-F_{x}' / F_{y}' :
y'=-(2 x sin(x+y)+x^{2 }cos(x+y)-5 y e^{x}) / (x^{2 }cos(x+y)-5 e^{x})

Answered by Lucia A.

Studies Engineering Degree at Exeter

Degrees are a made up unit; mathematicians simply decided that a complete revolution of a circle has 360 degrees, without that number actually meaning anything. Tecnically any number could have been picked to split a whole revolution into and, mathematically speaking, it would be just as valid as picking 360. On the other hand, radians split the circle into a number of segments that is not arbitrary: 2pi or around 6.283. Even though that number looks more complicated it makes more sense and it's actually related to what angles are. If you think about it, an angle is nothing more than how far you go around a circle. You can see this by looking at the length of the arc that you create when drawing a circle segment; the bigger the arc, the bigger your angle. You could draw the same segment of a circle with a bigger radius. The bigger you make the radius for that segment, the bigger you have to make the arc too, while the angle stays the same. If you look at these two quantities, arc length and radius, you will notice that the ratio between the two will always be the same if you keep the angle constant. So the ratio of arc length and radius after one half revolution actually gives you that fundamental number that shows up in everything that has to do with circles: pi. You might recognize that the equation to determine the perimeter of a circle is based on the same fundamental principle. One full revolution (perimeter) = 2pi * radius, or rewritten 2pi = perimeter/radius. Because the radian is intrinsically related to these basic geometric principles, it is much better to use in calculus and other areas of math as you move on.

Using the method of binomial expansion (which I will cover in more detail) we get
(2x-3y)^4 = + 1(2x)^4(3y)^0 - 4(2x)^3(3y)^1 + 6(2x)^2(3y)^2 - 4(2x)^1(3y)^3 + 1(2x)^0(3y)^4 =
= 16x^4 - 96x^3 y + 216x^2 y^2 - 216x y^3 + 81y^4
Note that we can get the coefficients 1, 4, 6, 4, 1 from Pascal's triangle, and since in the given example there is subtraction (2x-3y), there is a minus sign before each term that has 3y in an odd factor (^1, ^3 etc). You can simply remember to add a minus sign before every second term.
Now we see that in the term where y is in factor 3 as asked in the question (this is the term -216xy^3), the coefficient is -216. This is the answer we are looking for!

Answered by Davids M.

Studies Product Design Engineering at Glasgow

To find the derivative of any number to the power "x", such as 2^{x}, 5^{x}, or even 4.13^{x}, we first consider the general form a^{x}. We need to be a little creative here. We know that any variable y can be rewritten as e^{lny. } If we then say that y = a^{x} then we can say that y= e^{lna*x}. Note that this is because ln(a)^{x}=xlna. So that means y = a^{x} = e^{lna * x}. Now we want to find the derivative of a^{x}, or (e^{lna * x} )', which is lna* e^{x(lna)}. This is because lna is a definite number, and so we derivate this the same way we would e^{3x} (which would be 3*e^{3x}).
Now, if the derivative equals lna* e^{x(lna)} we see that actually, e^{x(lna)} is equal to y, so we can rewrite this further as lna*y. Since y = a^{x} we can simplify this finally to lna*a^{x}. That means that the derivative of a^{x} is a^{x}lna. This is the general form and should be remembered. So, (2^{x})'= 2^{x}ln2.

Company Information

Popular Requests

Other subjects

© MyTutorWeb Ltd 2013-2017

Terms & Conditions | Privacy Policy | Developed with Mercury1

mtw:mercury1:status:ok

Version: | 3.53.0 |

Build: | 35bfbfa47cfd-RR |

Time: | 2017-11-14T23:13:00Z |

Your message has been sent and you'll receive an email to let you know when responds.

Tutors typically reply within 24 hours.

Your message has been sent and you'll receive an email to let you know when responds.

Tutors typically reply within 24 hours.

Thanks , your message has been sent and we’ll drop you an email when replies. You should hear back within 24 hours.

After that, we recommend you set up a free, 15 minute meeting. They’re a great way to make sure the tutor you’ve chosen is right for you.

Thanks , your message has been sent and we’ll drop you an email when replies. You should hear back within 24 hours.

After that, we recommend you set up a free, 15 minute meeting. They’re a great way to make sure the tutor you’ve chosen is right for you.

**Limit reached ***(don't worry though, your email has still been sent)*

Now you've sent a few messages, we'd like to **give the tutors a chance to respond**.

Our team has been notified that you're waiting, but please contact us via

support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** if you're in a rush.

**Office hours are 8am to 7pm**, Monday to Friday, and we pick up emails on weekends.

Thanks,

The MyTutor team

**Limit reached ***(don't worry though, your email has still been sent)*

Now you've sent a few messages, we'd like to **give the tutors a chance to respond**.

Our team has been notified that you're waiting, but please contact us via

support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** if you're in a rush.

**Office hours are 8am to 7pm**, Monday to Friday, and we pick up emails on weekends.

Thanks,

The MyTutor team

**Limit exceeded ***(Your message will not be sent)*

You should have recieved a notification with your previous message, and **our team have also been notified that you're waiting.**

If you're in a rush, please contact us via support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** .

**Office hours are 8am to 7pm**, Monday to Friday. We also pick up emails on weekends.

Thanks,

The MyTutor team

**Limit exceeded ***(Your message will not be sent)*

You should have recieved a notification with your previous message, and **our team have also been notified that you're waiting.**

If you're in a rush, please contact us via support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** .

**Office hours are 8am to 7pm**, Monday to Friday. We also pick up emails on weekends.

Thanks,

The MyTutor team