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,