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.

NL
Answered by Nick12 L. Maths tutor

7613 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A line has an equation y = e^(2x) - 10e^(x) +12x, find dy/dx


Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.


Solve 4log₂(2)+log₂(x)=3


What are the roots of 3x^2 + 13x + 4 ?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences