Currently unavailable: for new students
Degree: Physics with Astrophysics (Masters) - Manchester University
Hi! My name is Jonny and I recently graduated with a 2:1 in a Master's degree (MPhys) in Physics with Astronomy from the University of Manchester.
Tutoring Experience: I have been a private tutor for 5 years, initially teaching GCSE Science and Maths and continuing on to A Level Maths and Physics for the last 4 years. I am also a qualified tutor with The Tutor Trust.
Flexibility and availability: I am generally very flexible and will endeavour to find a time that works around your busy schedule!
As a tutor, I aim to share my enthusiasm for science and maths with younger students, and to supplement the material they cover in school. As well as helping students to build confidence in their own abilities, I also strive to provide understanding as to why science and maths are important, and where the skills these subjects teach can be applied in the real world.
I understand the difficulty a student can have in understanding a particular topic, or solving a certain problem, and my lessons will provide a comfortable environment in which they can overcome these challenges. My experience as a tutor has taught me how to adapt to the individual needs of the student and teach in an engaging and enjoyable way.
So, if you think I can help, or you'd simply like to know a little more, please feel free to get in touch. I look forward to hearing from you!
|Further Mathematics||A Level||£26 /hr|
|Maths||A Level||£26 /hr|
|Physics||A Level||£26 /hr|
|Before 12pm||12pm - 5pm||After 5pm|
Please get in touch for more detailed availability
Andreas (Parent) August 15 2016
Jack (Student) June 7 2016
Andreas (Parent) April 15 2016
Emma (Parent) October 27 2015
Differentiation of arctan(x), also written tan^(-1)(x), requires a little knowledge of regular trigonometric algebra and differentiation, and implicit differentiation.
Let's set y = arctan(x) to start. Then, by the definition the arctan function, tan(y) = x. We recall the derivative of the tan function, d(tan(u))/du = (sec(u))^2.
So, if we differentiate both sides of our equation with respect to x, we find that (dy/dx)((sec(y))^2) = 1, using the rules of implicit differentiation. Now, we can rearrange our equation for dy/dx = 1/((sec(y))^2).
Thinking about some trigonometric algebra, we know that* (sec(y))^2 = 1 + (tan(y))^2. Additionally, remember that tan(y) = x as we said earlier! Using this information, simple substitution back into our equation yields dy/dx = 1/(1+x^2).
So, d(arctan(x))/dx = 1/(1+x^2).
*For a reminder of where this comes from, think about the trigonometric relation: (sin(y))^2 + (cos(y))^2 = 1.see more