Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 11

$f'(x)=24x^{-9}+\frac{1}{\sqrt x}$

$f(x)=-3x^{-8}+2\sqrt x=-3x^{-8}+2x^{\frac{1}{2}}$ Calculate the first derivative: $f'(x) =-3(-8)x^{-8-1}+2\left(\frac{1}{2}\right)x^{\frac{1}{2}-1}$ $f'(x) =24x^{-9}+x^{-\frac{1}{2}}$ $f'(x)=24x^{-9}+\frac{1}{\sqrt x}$