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OTHER CLASS XII TOPICS

Application of Integrals

Finding the area bounded by a curve

Applications of Derivatives

Applications of Derivatives

Increasing and Decreasing Functions

Maxima and Minima

Tangents and Normals

Continuity and Differentiability

Integration

Integration by Partial Fractions

Integration of Particular Functions

Integration using Trignometric Identities

Matrices

Diagonal Matrix

Finding the missing number in a Matrix

Identity Matrix

Probability

Relations and Functions

Equivalence Relation

Reflexive Relation

Symmetric Relation

Transitive Relation

Three Dimensional Geometry

Finding the direction cosines

Finding the equation of line

Finding the shortest distance

Trigonometry

Inverse Trigonometric Functions

Vector Algebra

Area of parallelogram

Finding the position vector of a point

Finding the unit vector

Mathematics Class XII Continuity and Differentiability Quotient Rule

Question

Find the derivative of $\dfrac{sin x}{x}$

$\dfrac{sin x - x cos x}{sin^2 x}$

$\dfrac{x cos x - sin x}{x^2}$

$\dfrac{x cos x - sin x}{sin^2 x}$

$cos x$

Solution

The correct answer is

$\dfrac{x cos x - sin x}{x^2}$

Explanation

Using the Quotient Rule,

$\dfrac{dy}{dx}$ =

$\dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx}}{v^2}$

$\dfrac{sin x}{x}$ =

$\dfrac{x D(sin x) - sinx D(x)}{x^2}$ =

$\dfrac{x cos x - sin x}{x^2}$