How do you find the derivatives of the function #f(x) = sin(x^2)#?

1 Answer
Apr 30, 2015

Use the chain rule, which says, for the sine function:

#d/dx(sinu)=cosu* (du)/dx#

(Or, if you prefer function notation:

For #f(x) = sin(g(x))#, the derivative is:

#f'(x) = cos(g(x)) *g'(x)#

So for this #f(x) = sin(x^2)#, we get

#f'(x) = cos(x^2)*2x = 2xcos(x^2)#

The question asks about the derivatives (plural). I'm not sure what you mean.
Do you also need the second derivative?, or a formula for the #n^(th)# derivative?, or perhaps it was just an error typing the question.