Open in App
Not now

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

• Last Updated : 11 Feb, 2021

### Question 1. If , prove that

Solution:

We have,

â‡’

Squaring both sides, we get,

y2 = x + y

### Question 2. If , prove that

Solution:

We have,

â‡’

Squaring both sides, we get,

y2 = cos x + y

â‡’

### Question 3. If , prove that

Solution:

We have,

â‡’

Squaring both sides, we get,

y2 = log x + y

### Question 4. If  , prove that

Solution:

We have,

â‡’

Squaring both sides, we get,

y2 = tan x + y

### Question 5. If  , prove that

Solution:

We have,

â‡’ y = (sin x)y

Taking log on both sides,

log y = log(sin x)y

â‡’ log y = y log(sin x)

### Question 6. If  , prove that

Solution:

We have,

â‡’ y = (tan x)y

Taking log on both sides,

log y = log(tan x)y

â‡’ log y = y log tan x

Differentiating with respect to x using chain rule,

Now,

### Question 7. If  , prove that

Solution:

We have,

â‡’ 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,

â‡’ y = (cos x)y

Taking log on both sides,

log y = log(cos x)y

â‡’ log y = y log (cos x)

Differentiating with respect to x using chain rule,

My Personal Notes arrow_drop_up
Related Articles