Find the first and second derivative of the function f(x)=e^x-x^5

Question

please help

Answer 1

First thing to do is to review the relevant properties of derivatives.

 

The derivative of e^x is just e^x.

 

To take the derivative of x to a power, bring the power down and then lower it by one.

 

Since there's a subtraction symbol between the two terms, we can take the derivative of each term separately.

 

f'(x) = e^x - 5x^4

 

f''(x) = e^x - 20x^3

 

In calculating the second derivative, we bring down the 4 from the first derivative and multiply it with the 5 that was already there, giving us the 20.