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?
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 .