## Calculus: Early Transcendentals 8th Edition

$f(x)=e^x-x^3$ $f'(x)=e^x-3x^2$ $f''(x)=e^x-6x$
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.