Question

Derivative of x² w.r.t. x³ is:
1. \(\rm \frac{1}{\sqrt x}\)
2. √x
3. 0
4. \(\rm \frac{2}{3x}\)

Answer 1

Correct Answer - Option 4 : \(\rm \frac{2}{3x}\)

Concept:

Chain Rule of Derivatives: For two functions u and v of x, we have: \(\rm \frac{du}{dv}=\frac{du}{dx}\times\frac{dx}{dv}\).

 

Calculation:

Using the chain rule of derivatives, we have:

\(\rm \frac{dx^2}{dx^3}=\frac{dx^2}{dx}\times\frac{dx}{dx^3}\)

= \(\rm \frac{dx^2}{dx}\times \frac 1 {\frac{dx^3}{dx}}\)

= \(\rm \frac{2x}{3x^2}\)

= \(\rm \frac{2}{3x}\)