Question

Finding second Derivatives In Exercise,find the second derivate.
f(x) = 5e - x - 2e - 5x

Answer 1

Answer: The second derivative would be

`f''(x)=5e^(-x)-50e^(-5x)`

Explanation:

Since we have given that

`f(x)=5e^(-x)-2e^(-5x)`

We will find the first derivative w.r.t. 'x'.

So, it becomes,

`f'(x)=-5e^(-x)+10e^(-5x)`

Then, we will find the second derivative w.r.t 'x'.
`f''(x)=5e^(-x)+10* -5e^(-5x)\\\\f''(x)=5e^(-x)-50e^(-5x)`

Hence, the second derivative would be

`f''(x)=5e^(-x)-50e^(-5x)`