**Chapter 1 Differentiation Ex 1.4**

## Chapter 1 Differentiation Ex 1.4

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

(ii) x = a cot θ, y = b cosec θ

Solution:

x = a cot θ, y = b cosec θ

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

(iv) x = sin θ, y = tan θ

Solution:

x = sin θ, y = tan θ

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

(v) x = a(1 – cos θ), y = b(θ – sin θ)

Solution:

x = a(1 – cos θ), y = b(θ – sin θ)

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

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

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

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

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

(iv) x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t =

Solution:

x = 2 cos t + cos 2t, y = 2 sin t – sin 2t

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

(v) x = t + 2 sin(πt), y = 3t – cos(πt) at t =

Solution:

x = t + 2 sin(πt), y = 3t – cos(πt)

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

Question 3.

log x = (sin 3t)(log e), log y = (cos 3t)(log e)

log x = sin 3t, log y = cos 3t ….. (1) [∵ log e = 1]

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

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

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

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

Question 4.

(i) Differentiate x sin x w.r.t tan x.

Solution:

Let u = x sinx and v = tan x

Then we want to find

Differentiating u and v w.r.t. x, we get

Solution:

(v) Differentiate 3x w.r.t. log_{x}3.

Solution:

Differentiating u and v w.r.t. x, we get

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