mathematics: analysis and approaches sl>Differential Calculus>Differential Calculus 2>Differentiation Rules

Differentiation Rules

IMPORTANT

Differentiation Rules: Overview

This Topic covers sub-topics such as Quotient Rule in Differentiation, Product Rule in Differentiation, Finding Higher Order Derivatives and, Chain Rule for Differentiation of Composite Functions

Important Questions on Differentiation Rules

HARD

IMPORTANT

mathematics: analysis and approaches sl>Differential Calculus 2>Differentiation Rules> Q 1

If $(x - a)^{2} + (y - b)^{2} = c^{2}$ , prove that $\frac{{[1 + {(\frac{d y}{d x})}^{2}]}^{\frac{3}{2}}}{\frac{d^{2} y}{d x^{2}}}$ is a constant independent of $a$ and $b$ .

HARD

IMPORTANT

mathematics: analysis and approaches sl>Differential Calculus 2>Differentiation Rules> Q 2

$y = x^{x}$ , prove that $\frac{d^{2} y}{d x^{2}} - \frac{1}{y} {(\frac{d y}{d x})}^{2} - \frac{y}{x} = 0$

HARD

IMPORTANT

mathematics: analysis and approaches sl>Differential Calculus 2>Differentiation Rules> Q 3

If $y = \log \{x + \sqrt{x^{2} + a^{2}}\}$ , prove that $(x^{2} + a^{2}) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} = 0$

HARD

IMPORTANT

mathematics: analysis and approaches sl>Differential Calculus 2>Differentiation Rules> Q 4

If $y = x \log (\frac{x}{a + b x})$ , prove that $x^{3} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{2}$

HARD

IMPORTANT

mathematics: analysis and approaches sl>Differential Calculus 2>Differentiation Rules> Q 5

If $y = A \cos (\log x) + B \sin (\log x)$ , prove that $x^{2} \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + y = 0$ .