Derivative of x3 + 1 with respect to x2

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Derivative of x³ + 1 with respect to x² + 1 is

Options:

$\frac{2 x}{3}$

$\frac{x}{3}$

$\frac{x}{2}$

$\frac{3 x}{2}$

Correct Answer:

$\frac{3 x}{2}$

Explanation:

$z = x^3+1$ $y = x^2+1$

$\frac{dz}{dx} = 3x^2$ $\frac{dy}{dx} = 2x$

so $\frac{dz/dx}{dy/dx} = \frac{dz}{dy} = \frac{3x^2}{2x}$

so $\frac{d(x^3+1)}{d(x^2+1)} =\frac{3x}{2} $

Option: 4