Question

What is the derivative of \(7\sqrt[3]{x}-\frac{3}{x^4}+5x\) with respect x?

(a) \(7x^{\frac{-1}{3}}-3x^{-5}+5\)

(b) \(7x^{\frac{-2}{3}}-3x^{-5}+5\)

(c) \(7x^{\frac{-2}{3}}-3x^{-3}+5\)

(d) \(7x^{\frac{-1}{3}}-3x^{-3}+5\)

The question was posed to me in unit test.

My question comes from Total Derivative in section Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (b) \(7x^{\frac{-2}{3}}-3x^{-5}+5\)

The best explanation: Given: y= \(7\sqrt[3]{x}-\frac{3}{x^4}+5x\)

\(\frac{dy}{dx}=\frac{d(7x^{\frac{-1}{3}}-3x^{-4}+5x)}{dx}\)

\(\frac{dy}{dx}=7x^{\frac{-1}{3}-1}-3x^{-4-1}+5x^{1-1}\)

\(\frac{dy}{dx}=7x^{\frac{-2}{3}}-3x^{-5}+5\)