MYTUTOR SUBJECT ANSWERS

187 views

Given that y = 5x^2 - 4/(x^3), x not equal to 0, find dy/dx.

y = 5x2 - 4/x3

1/x can be written as x-1, which means our equation can also be written as y = 5x2 - 4x-3.

dy/dx means that we need to differentiate y in terms of x.

To differentiate an equation, we need to multiply the coefficient (the number before the x) by its power (the smaller number above it), and then subtract 1 from the power. This must be done for all parts of the equation.

We can split up the equation and do the working bit by bit, so first lets look at "5x2":

Multiplying the coefficient by the power, we get 5 X 2 = 10, and then 2 - 1 = 1, which means the differential of 5x2 is 10x1, and the ^1 can be dropped to get 10x.

Looking at the second part "-4x-3":

-4 X -3 = 12, and -3 - 1 = -4, so the differential of -4x-3 is 12x-4, which can also be written as 12/x4 (reversing the rule we used earlier).

So putting the two parts back together, we get dy/dx = 10x + 12/x4.

It is also important to note that the question specified x is not equal to 0, and this is due to the fact that division by 0 can have a significant effect on an equation, with any number divided by 0 equalling infinity, a very difficult number to quantify or use.

Nick L. A Level Maths tutor, GCSE Maths tutor

5 months ago

Answered by Nick, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

257 SUBJECT SPECIALISTS

£20 /hr

Georgiana P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths

Maths

“I am a Maths student at the University of Bristol and hope to share my love of maths with you. I believe that Maths is learnt in 3 steps:    1) I will explain and we will discuss the main principles of what we are working on, assis...”

£20 /hr

Kavita R.

Degree: chemistry (Bachelors) - Warwick University

Subjects offered: Maths, Economics+ 1 more

Maths
Economics
Chemistry

“As Mister Pip highlights, the positive externalises of education are endless, thus I wish to embed optimism, hard work and dedication within individuals.”

MyTutor guarantee

£30 /hr

Daniel K.

Degree: Mathematical and Theoretical Physics (Masters) - Oxford, Merton College University

Subjects offered: Maths, Science+ 5 more

Maths
Science
Physics
Further Mathematics
Chemistry
.MAT.
-Personal Statements-

“Mathematics, Merton College, University of Oxford. I enjoy sharing my experience and enthusiasm in Maths with those who could do with some help”

About the author

Nick L.

Currently unavailable: for regular students

Degree: Mathematics and Computer Science (Masters) - York University

Subjects offered: Maths

Maths

“About Me: I am a student at the University of York, currently in my third year of a 4 year Masters course studying Mathematics and Computer Science. I have a strong interest in both halves of this joint honours course but my main pass...”

You may also like...

Other A Level Maths questions

What is a complex number?

How to integrate by parts

What is a 'derivative'?

What is the importance of the Central Limit Theorem in carrying out hypothesis tests?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok