Find the derivative of f(x) = \frac{-1}{\sqrt{2x}} + 2x a. f'(x) = 2 - \frac{1}{\sqrt{2}x^2} ...

Question:

Find the derivative of {eq}f(x) = \frac{-1}{\sqrt{2x}} + 2x {/eq}.

a. {eq}f'(x) = 2 - \frac{1}{\sqrt{2}x^2} {/eq}

B. {eq}f'(x) = - \frac{1}{\sqrt{2}x^2} {/eq}

C. {eq}f'(x) = \frac{1}{\sqrt{2}x^2} {/eq}

D. {eq}f'(x) = 2 + \frac{1}{\sqrt{2}x^2} {/eq}

{eq}\displaystyle f(x) = \frac{-1}{\sqrt{2x}} + 2x {/eq}

Power formula is an important formula of the derivatives.

We will use this formula for the derivative which is

{eq}\displaystyle \frac{\mathrm{d} }{\mathrm{d} x}x^n=nx^{n-1}\\ \displaystyle f'(x)=\frac{1}{2\sqrt{2}x^{\frac{3}{2}}}+2 {/eq}