Question

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

Answer 1

Answer: The second derivative would be

$f''(x)=5e^{-x}-50e^{-5x}$

Step-by-step 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'.$f''(x)=5e^{-x}+10\times -5e^{-5x}\\\\f''(x)=5e^{-x}-50e^{-5x}$

Hence, the second derivative would be

$f''(x)=5e^{-x}-50e^{-5x}$