Problems on differentiation class 11 physics

 

Questions on Differentiation (With Answers)

Here are a few solved questions based on differentiation concept.

1. Differentiate x5 with respect to x.

Solution: Given, y = x5

On differentiating w.r.t we get;

dy/dx = d(x5)/dx

y’ = 5x5-1 = 5x4

Therefore, d(x5)/dx = 5x4

2. Differentiate 10x2 with respect to x.

Solution: y = 10x2

y’ = d(10x2)/dx

y’ = 2.10.x = 20x

Therefore, d(10x2)/dx = 20 x

3. Differentiate 20x-4 + 9.

Solution: y = 20x-4 + 9

y’ = d(20x-4 + 9)/dx

y’ = d(20x-4)/dx + d(9)/dx

y’ = -4.20.x-4-1+0

y’ = -80x-5

Therefore, d(20x-4 + 9)/dx = -80x-5

4. Differentiate sin(3x+5)

Solution: Say, y = sin (3x+5)

dy/dx = d[sin(3x+5)]/dx

= cos (3x+5) d(3x+5)/dx [ By chain rule]

= cos (3x+5) [3]

y’ = 3 cos (3x+5)

d[sin(3x+5)]/dx = 3 cos (3x+5)

5. Differentiate tan2x.

Solution: Say, y = tan2x

dy/dx = d(tan2x)/dx

= 2tan2-1x. d(tan x)/dx

= 2tan x sec2x

d[tan2x]/dx = 2tan x sec2x

6. Compute the derivative of f(x) = sin2x.

Solution: f(x) = sin2x = sin x sin x

= d(sin x)/dx. sin x + sin x.d(sin x)/dx

= cos x. sin x + sin x cos x

= 2 sin x cos x

Practice Questions

Here are some more questions which students can practice.

Differentiate the following:

1. etan x                                        [Ans: etan x sec2x]

2. Sin2 (2x + 1)                   [Ans: 2sin(4x+2)]

3. log7 (2x – 3)                   [Ans: 2/{(2x-3)log 7}]

4. logx 3                               [Ans: -1/{xlog3(log3x)2}]

5. 3xlogx                                     [Ans: 3xlogx.log 3(1+log x)]

6. (x+1)/x                           [Ans:  -1/x2]

7. (x-a)(x-b)                       [Ans: 2x-(b+a)]

8. 3cot x+5cosec x            [Ans: −cosec x(3cosec x+5cot x)