Find f '(x) and f ''(x). f(x) = x^5e^x

Question

Please help me 

Answer 1

f(x) = x⁵e^x

 

 

We need to use a combination of product rule and chain rule to find the derivative.  Also, the derivative of e^x is always e^x.

 

f'(x) = 5x⁴e^x + x⁵e^x

 

 

 

To find the second derivative, take the derivative of the first derivative.

 

f''(x) = (20x³e^x + 5x⁴e^x) + (5x⁴e^x + x⁵e^x)

 

 

I leave it up to you simplify the derivative.