Class 12 RD Sharma Solutions - Chapter 11 Differentiation - Exercise 11.2 | Set 1

Question 1. Differentiate y = sin (3x + 5) with respect to x.

Solution:

We have,

y = sin (3x + 5)

On differentiating y with respect to x we get,

On using chain rule, we have

Question 2. Differentiate y = tan² x with respect to x.

Solution:

We have,

y = tan² x

On differentiating y with respect to x we get,

On using chain rule, we have

Question 3. Differentiate y = tan (x + 45°) with respect to x.

Solution:

We have,

y = tan (x + 45°)

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 4. Differentiate y = sin (log x) with respect to x.

Solution:

We have,

y = sin (log x)

On differentiating y with respect to x we get,

On using chain rule, we have

Question 5. Differentiate y = e^{sin √x}with respect to x.

Solution:

We have,

y = e^{sin √x}

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

Question 6. Differentiate y = e^{tan x} with respect to x.

Solution:

We have,

y = e^{tan x}

On differentiating y with respect to x we get,

On using chain rule, we have

Question 7. Differentiate y = sin² (2x + 1) with respect to x. 

Solution:

We have,

y = sin² (2x + 1)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

As sin 2A = 2 sin A cos A, we get

Question 8. Differentiate y = log₇ (2x − 3) with respect to x.

Solution:

We have,

y = log₇ (2x − 3)

As , we have

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 9. Differentiate y = tan 5x° with respect to x.

Solution:

We have,

y = tan 5x°

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 10. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 11. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 12. Differentiate y = log_x 3 with respect to x.

Solution:

We have,

y = log_x 3

As , we get

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

As , we get

Question 13. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 14. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 15. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 16. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 17. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 18. Differentiate y = (log sin x)² with respect to x.

Solution:

We have,

y = (log sin x)²

On differentiating y with respect to x we get,

On using chain rule, we have

Question 19. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

Question 20. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

Question 21. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using product rule, we have

On using chain rule, we have

Question 22. Differentiate y = sin(log sin x) with respect to x.

Solution:

We have,

y = sin(log sin x)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

Question 23. Differentiate y = e^{tan 3x} with respect to x.

Solution:

We have,

y = e^{tan 3x}

On differentiating y with respect to x we get,

On using chain rule, we have

Question 24. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Summary

Exercise 11.2 | Set 1 focuses on applications of derivatives. It covers topics such as finding the rate of change, velocity and acceleration problems, and optimization. Students are expected to apply differentiation techniques to solve real-world problems, interpret the meaning of derivatives in various contexts, and use derivatives to find maximum and minimum values of functions.