Question

Use the formal definition of derivative here:
Find f'(x) if \[f(x)=sqrt{x^4-x}+2\].

Answer 1

\[f(x)=\sqrt{x^4-x}+2\]

Answer 2

\[f'(x)=\frac{d}{dx}\sqrt{x^4-x}+ \frac{d}{dx}(2)\]\[f'(x)= \frac{1}{2\sqrt{x^4-x}} \frac{d}{dx}(x^4-x)+ 0\]\[f'(x)= \frac{1}{2\sqrt{x^4-x}} (4x^3-1) \ or \ f'(x)= \frac{4x^3-1}{2\sqrt{x^4-x}} \]