# Trigonometric differentiation

When y=sin(pi*x), why does y'=cos(pi*x)*pi, not y'=cos(pi*x)?

hk

## Answers and Replies

Integral
Staff Emeritus
Science Advisor
Gold Member
It's the chain rule. when the argument of a trig function is a FUNCTION of x, you have take the derivative of the agrgument. So, in general

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

So than in this case y=f(u)=sinu and u=g(x)=pi*x, correct?

OlderDan
Science Advisor
Homework Helper
h_k331 said:
So than in this case y=f(u)=sinu and u=g(x)=pi*x, correct?
That is correct.

Thanks guys, I appreciate it.

hk