Differentiate: y = xsin(x)

  • Google+ icon
  • LinkedIn icon
  • 9468 views

This is a function which is in the form, 

y = f(x)g(x)

It's the product of two functions and so we must make use of the product rule. This is a simple formula which you have to remember:

dy/dx = f'(x)g(x) + f(x)g'(x).

In words: the derivative of first function multiplied by the original second function, plus, the derivative of the second function multiplied by the original first function.

In this question,

f(x) = x

g(x) = sin(x)

so we can find that, 

f'(x) = 1

g'(x) = cos(x)

and by substituting this into the formula for the product rule we get the answer:

dy/dx = sin(x) + xcos(x).

Oliver R. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathema...

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