Question

Derivative of f(x) = -3 x^5 sqrt[x] + 4/(x^2 sqrt[x])

Answer 1

\[f(x) = -3x^5 \sqrt{x} + \frac{ 4 }{ x^2 \sqrt{x} }\]

Answer 2

It looks tedious since it involves product and quotient rule. Anyway, what is the product and quotient rule formulas?

Answer 3

Actually, sum rule and power rule is only needed here.

See: \(\large x^n\sqrt{x} = x^nx^{1/2} = x^{n+1/2}\)

Answer 4

For second term, just remember that \(\dfrac{1}{x^n} = x^{-n}\)

Answer 5

Sum Rule: \(\dfrac{d}{dx}[f(x)\pm g(x)] = f'(x)\pm g'(x)\)

Power Rule: \(\dfrac{d}{dx}x^n = nx^{n-1}\)

Answer 6

@4586Jen Does that help?