Question

What is the second derivative of `f(x)= e^sqrt(3x-7)`?

Answer 1

`f''(x)=(((2sqrt(3x-7))* 9/2e^sqrt(3x-7)(3x-7)^(-1/2))-3e^(sqrt(3x-7)) *3(3x-7)^(-1/2))/(4(3x-7))`

Explanation:

By use of the chain rule, power rule, and quotient rule, we get :

`f'(x)=e^(sqrt(3x-7)) * 1/2(3x-7)^(-1/2) * (3)`

`=(3e^(sqrt(3x-7)))/(2sqrt(3x-7))`.

`therefore f''(x)=(((2sqrt(3x-7))* 9/2e^sqrt(3x-7)(3x-7)^(-1/2))-3e^(sqrt(3x-7)) *3(3x-7)^(-1/2))/(4(3x-7))`