Answer
$f(x)=e^x-x^3$
$f'(x)=e^x-3x^2$
$f''(x)=e^x-6x$
Work Step by Step
Let's first remember the power rule:
$f(x)=x^n$
$f'(x)=nx^{n-1}$
And we also know that $\frac{d}{dx}[e^x]=e^x$
So with this information, we can find the first and second derivatives.
We know that $f(x)=e^x-x^3$
So by using the power rule and the differentiation of an exponential function, we can find that:
$f'(x)=e^x-3x^2$
And by taking the derivative of that, we can find the second derivative:
$f''(x)=e^x-6x$
So now you now that
$f(x)=e^x-x^3$
$f'(x)=e^x-3x^2$
$f''(x)=e^x-6x$
You can graph each equation together to make sure these answers are reasonable.
