How exactly would one go about using the power rule to solve this problem?
I'm trying to find the best method, in preparation for a test this week.
The power rule: $\displaystyle \frac{d}{dx}x^{n}=nx^{n-1}$
a) $\displaystyle f(x)=2x^{2}+3x-x^{-1}$
Using the power rule:
$\displaystyle f'(x)=(2)(2)x^{2-1}+(1)(3)x^{1-1}-(-1)x^{-1-1}$
$\displaystyle f'(x)=4x+3+\frac{1}{x^{2}}$
b)$\displaystyle f(x)=x+x^{-\frac{1}{2}}$
Using the power rule:
$\displaystyle f'(x)=(1)x^{1-1}+(-\frac{1}{2})x^{-\frac{3}{2}}$
$\displaystyle f'(x)=1-\frac{1}{2\sqrt{x^{3}}}$