I am having some issues with Derivatives. My first question is what is the derivative of e^4x? I know one of the rules is (e^x)' = e^x. Then why is (e^4x)' not e^4x?

Thanks

Adam

Printable View

- Nov 17th 2012, 02:13 PMxRockbottomxDerivatives
I am having some issues with Derivatives. My first question is what is the derivative of e^4x? I know one of the rules is (e^x)' = e^x. Then why is (e^4x)' not e^4x?

Thanks

Adam - Nov 17th 2012, 02:16 PMMacstersUndeadRe: Derivatives
You have to apply what is known as the Chain Rule in the case of e^4x. The Chain rule is f(g(x))' = f'(g(x)) * g'(x). f'(x) = e^x , g(x) = 4x, g'(x) = 4

(e^4x)' = e^4x * 4 = 4e^4x - Nov 17th 2012, 02:28 PMxRockbottomxRe: Derivatives
When do you use the chain rule?

- Nov 17th 2012, 02:29 PMxRockbottomxRe: Derivatives
and thank you

- Nov 17th 2012, 03:16 PMMacstersUndeadRe: Derivatives
You use the chain rule whenever you are faced with a form like f(g(x)) and you know the derivative of f(x) and g(x)

- Nov 17th 2012, 04:41 PMProve ItRe: Derivatives
Another (easier) way to write the chain rule is . So you let your "inner" function of x be u, so that you can then write your function y in terms of u, take the derivative of each, then convert back to a multiple of x and multiply them.

For example, if our function was , our "inner" function is leaving .

Differentiating each gives and .

Therefore the derivative is .