Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

# Differentiate of the Following from First Principle: Sin (X + 1) - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Differentiate of the following from first principle:

(−x)−1

Advertisement Remove all ads

#### Solution

$\left( - x \right)^{- 1} = \frac{1}{- x}$
$\frac{d}{dx}\left( f\left( x \right) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}$
$\frac{d}{dx}\left( \frac{1}{- x} \right) = \lim_{h \to 0} \frac{\frac{1}{- \left( x + h \right)} - \frac{1}{- x}}{h}$
$= \lim_{h \to 0} \frac{\frac{- 1}{x + h} + \frac{1}{x}}{h}$
$= \lim_{h \to 0} \frac{- x + x + h}{h x \left( x + h \right)}$
$= \lim_{h \to 0} \frac{h}{h x \left( x + h \right)}$
$= \lim_{h \to 0} \frac{1}{x \left( x + h \right)}$
$= \frac{1}{x . x}$
$= \frac{1}{x^2}$

Concept: The Concept of Derivative - Algebra of Derivative of Functions
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.2 | Q 2.06 | Page 25

#### Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?