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

Question 1. If , prove that 

Solution:

We have, 

⇒ 

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,