# Sine Function Derivative

• Feb 15th 2010, 11:36 AM
Jools
Sine Function Derivative
Hey folks. I have a question here...

Determine the derivative of the following function:

f(x) = sin(e^x)

I know that f '(x) = cosx... but I'm having a hard time putting it together.

Thanks!
• Feb 15th 2010, 11:40 AM
mathemagister
Quote:

Originally Posted by Jools
Hey folks. I have a question here...

Determine the derivative of the following function:

f(x) = sin(e^x)

I know that f '(x) = cosx... but I'm having a hard time putting it together.

Thanks!

Do you know the chain rule?

\$\displaystyle f(x) = f(g(x))\$
\$\displaystyle f'(x) = f'(g(x)).g'(x)\$

\$\displaystyle f(x) = sin(e^x)\$
\$\displaystyle f'(x) = cos(e^x).e^x\$

This should make sense if you are familiar with the chain rule.
• Feb 15th 2010, 11:42 AM
e^(i*pi)
Use the chain rule and note that the derivative of e^x is e^x

Spoiler:
\$\displaystyle e^x \, cos(e^x)\$
• Feb 15th 2010, 11:50 AM
Jools
Quote:

Originally Posted by e^(i*pi)
Use the chain rule and note that the derivative of e^x is e^x

Spoiler:
\$\displaystyle e^x \, cos(e^x)\$

Ok... Got it I think. Thanks.