Question

What is the derivative of $x^3$ with respect to $x^2$?

• A. $3x^2$
• B. $\frac{3x}{2}$
• C. $x$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{3x}{2}$

Derivative of $x^3$ is $\frac{d}{dx}{(x}^3)=3x^2$

Derivative of $x^2$ is $\frac{d}{dx}{(x}^2)=2x$

So derivative of $x^3$ with respective $x^2$ is $\left[\frac{d}{dx}{(x}^3\right)]/\left[\frac{d}{dx}{(x}^2\right)]=\frac{3x^2}{2x}=\frac{3x}{2}$