A curve has equation y = 4x + 1/(x^2) find dy/dx.

  • Google+ icon
  • LinkedIn icon
  • 883 views

As in every case dy/dx can be found by differentiating each term individually with respect to x.

Let's first tackle the 4x term.

As always the derivative can be found by multiplying the term by the power of x and reducing the power of x by 1. i.e. axb -> abxb-1

In this case b is simply equal to 1 because x=x1. Therefore the derivative of 4x with respect to x is given by 1*4x= 4*1 = 4.

Next let's tackle the 1/x2 term.

In order to use the same method as previously we must first write 1/xas a power of x i.e. in the familiar form axb.

From the laws of indices: recall that x-b=1/xb. In this example b is simply equal to 2 so 1/x2=x-2.

Now that we have written the term in the form axb we can apply the same method as previously i.e.   x-2-> -2x-3.

Finally collecting both the terms we have arrived at the result that dy/dx is -2x-3+4.

Callum H. A Level Maths tutor, GCSE Maths tutor, A Level Economics tu...

About the author

is an online A Level Maths tutor with MyTutor studying at Bristol University

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

95% of our customers rate us

Browse tutors

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

mtw:mercury1:status:ok