**Chapter 1 Differentiation Ex 1.5**

## Chapter 1 Differentiation Ex 1.5

**Question 1.Find the second order derivatives of the following:**

**(ii) . tan xSolution:Let y = . tan x**

**(iii) . cos 5xSolution:Let y = . cos 5x**

**(iv) . log xSolution:Let y = . log x**

**(v) log(log x)Solution:Let y = log(log x)**

**(vi) Solution:y = **

log y = log = x log x

Differentiating both sides w.r.t. x, we get

**Question 2.**

**(ii) x = 2a, y = 4atSolution:x = 2a, y = 4at**

Differentiating x and y w.r.t. t, we get

Solution:

x = sin Î¸, y = Î¸

Differentiating x and y w.r.t. Î¸, we get,

Solution:

x = a cos Î¸, y = b sin Î¸

Differentiating x and y w.r.t. Î¸, we get

**Question 3.**

Differentiating x and y w.r.t. t, we get

Solution:

y = x + tan x

Solution:

Differentiating both sides w.r.t. x, we get

Differentiating both sides w.r.t. x, we get

**(x) If y = log(log 2x), show that x + (1 + x) = 0.Solution:y = log(log 2x)**

Differentiating both sides w.r.t. x, we get

**Solution:**
x = a sin t â€“ b cos t, y = a cos t + b sin t

Differentiating x and y w.r.t. t, we get

**Question 4.Find the nth derivative of the following:(i) (ax + Solution:**

Let y = (ax +

**(ii) 1/xSolution:Let y = 1/x**

**(iii) Solution:Let y = **

**(iv) Solution:Let y = **

**(v) log(ax + b)Solution:**

Let y = log(ax + b)

**(vi) cos xSolution:Let y = cos x**

**(vii) sin(ax + b)Solution:Let y = sin(ax + b)**

**(viii) cos(3 â€“ 2x)Solution:**

**(ix) log(2x + 3)Solution:**

**(xi) y = . cos (bx + c)Solution:y = . cos (bx + c)**

**(xii) y = . cos (6x + 7)Solution:**