# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.6

• Last Updated : 11 Feb, 2021

### Question 1. If , prove that Solution:

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⇒ Squaring both sides, we get,

y2 = x + y ### Question 2. If , prove that Solution:

We have, ⇒ Squaring both sides, we get,

y2 = cos x + y

⇒ ### Question 3. If , prove that Solution:

We have, ⇒ Squaring both sides, we get,

y2 = log x + y ### Question 4. If , prove that Solution:

We have, ⇒ Squaring both sides, we get,

y2 = tan x + y ### Question 5. If , prove that Solution:

We have, ⇒ y = (sin x)y

Taking log on both sides,

log y = log(sin x)y

⇒ log y = y log(sin x) ### Question 6. If , prove that Solution:

We have, ⇒ y = (tan x)y

Taking log on both sides,

log y = log(tan x)y

⇒ log y = y log tan x

Differentiating with respect to x using chain rule, Now, ### Question 7. If , prove that Solution:

We have, ⇒ y = u + v + w where Now, Taking log on both sides, Differentiating with respect to x, Taking log on both sides, Taking log on both sides Using equation in equation (i), we get ### Question 8. If , Prove that Solution:

We have, ⇒ y = (cos x)y

Taking log on both sides,

log y = log(cos x)y

⇒ log y = y log (cos x)

Differentiating with respect to x using chain rule, My Personal Notes arrow_drop_up