Okay, I am starting to get this (I copied and passted the response I got the fir

Question

Okay, I am starting to get this (I copied and passted the response I got the first time, which is helpful, but I'm still not getting it exactly....as to what is what in the chain rule here

Can someones show me the steps you take to get derivative of: 5e3x^4 No need to simplify all the way, just need steps. For example, I know I need to use the chain rule, but when I do this I get 60 (e3x)3 and that is wrong. Thanks!

Comment Expert Answer:

f(x) = 5e3x^4 ==> f '(x) = 5e3x^4 (3(4)x4-1)

since d/dx ex = ex ; d/dx f(g(x)) = f '(g(x)) g '(x) ==> f '(x) = 60x3e3x^4

Thank you!! so what are the inner and outer functions exactly? From what you're saying g(x)=3x^4, so that would make f(x) 5e and the derivative of 5e is 0.....so I'm still a little confused.

Explanation / Answer

f(x) = 5e^(3x^4)

let t = 3x^4

f(t) = 5e^(t)

d(f(x))/dx = (d(f(t))/dt) * (dt/dx)      (chain rule)

dt/dx = 12x^3

(d(f(t))/dt) = 5e^(t)

so d(f(x))/dx = 60x^3.e^(t) = 60x^3.e^(3x^4)

Hope you get this.

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