Sine Function Derivative

• February 15th 2010, 12:36 PM
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!
• February 15th 2010, 12:40 PM
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?

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

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

This should make sense if you are familiar with the chain rule.
• February 15th 2010, 12:42 PM
e^(i*pi)
Use the chain rule and note that the derivative of e^x is e^x

Spoiler:
$e^x \, cos(e^x)$
• February 15th 2010, 12:50 PM
Jools
Quote:

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

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

Ok... Got it I think. Thanks.