Question

How do you find the derivative of `(2e^(3x) + 2e^(-2x))^4`?

Answer 1

`4(2e^(3x)+2e^(-2x))^3(6e^(3x)-4e^(-2x))`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larr" chain rule"`

`f(g(x))=(2e^(3x)+2e^(-2x))^4`

`rArrf'(g(x))=4(2e^(3x)+2e^(-2x))^3`

`g(x)=2e^(3x)+2e^(-2x)`

`rArrg'(x)=2e^(3x).d/dx(3x)+2e^(-2x).d/dx(-2x)`

`color(white)(rArrg'(x))=6e^(3x)-4e^(-2x)`

`rArrdy/dx=4(2e^(3x)+2e^(-2x))^3(6e^(3x)-4e^(-2x))`