Differentiate the following function: a + b cos x sin x

Given: a + b cos x sin x We know that, from quotient rule d d x u v = v d u d x - u d v d x v 2 Now, d d x a + b cos x sin x = sin x d d x ( a + b cos x ) - ( a + b cos x ) d d x sin x sin 2 x = 0 + sin x ( - b sin x ) - ( a + b cos x ) cos x sin 2 x = - b sin 2 x - a cos x - b cos 2 x sin 2 x = - b ( 1 ) - a cos x sin 2 x Therefore, d d x a + b cos x sin x = - cosec x ( a cot x + b cosec x ) .

If y = x + 1 x , show that 2 x · d y d x + y = 2 x

To show: 2 x · dy dx + y = 2 x We know that, d d x x n = n x n - 1 . Now, differentiating with respect to x , d y d x = d d x x + 1 x = d d x x 1 2 + x - 1 2 = 1 2 x - 1 2 x - 3 2 Now, LHS = 2 x · d y d x + y = 2 x × 1 2 x - 1 2 x 3 2 + x + 1 x = x - 1 x + x + 1 x = 2 x . ∴ LHS = RHS

If y = x a + a x , prove that ( 2 x y ) d y d x = x a - a x

To prove: ( 2 x y ) d y d x = x a - a x We know that, d d x x n = n x n - 1 . Differentiating y = x a + a x with respect to x , d y d x = d d x x a + a x = 1 2 a x - a 2 x 3 2 Now, LHS = ( 2 x y ) d y d x = 2 x x a + a x 1 2 ax - a 2 x 3 2 = x a + a x x a - a x = x a - a x ∴ LHS = RHS

E M B I B E

WBCHSE Mathematics for Class 11>Calculus>Chapter 24 - Differentiation>EXERCISE 2A

R S Aggarwal Solutions for Exercise 1: EXERCISE 2A

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 1: EXERCISE 2A

Attempt the practice questions from Exercise 1: EXERCISE 2A with hints and solutions to strengthen your understanding. WBCHSE Mathematics for Class 11 solutions are prepared by Experienced Embibe Experts.