How do I find a second derivative?

Question

What is the second derivative for the function y=e^(6-x^2) ? Please show workings.

Answer 1

y = e^{6 - x^2}

 

let z = 6 - x²

dz/dx = -2x

 

start with first derivative y' = e^z(-2x)            this used the chain rule

 

for second derivative we use product rule

 

y'' = e^z(-2) + (-2x) e^z(-2x) = 2e^z (2x² - 1) = 2 (2x² - 1) e6 ^{- x^2}

Answer 2

Please type your function again. You have question marks instead of regular symbols.