# 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 = tan**^{2} x with respect to x.

^{2}x with respect to x.

**Solution:**

We have,

y = tan

^{2}xOn differentiating y with respect to x we get,

On using chain rule, we have

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

**Solution:**

We have,

y = tan (x + 45Â°)

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 âˆšx} **with respect to x.**

^{sin âˆšx}

**Solution:**

We have,

y = e

^{sin âˆšx}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.

^{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 = sin**^{2} (2x + 1) with respect to x.

^{2}(2x + 1) with respect to x.

**Solution:**

We have,

y = sin

^{2}(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 = log**_{7} (2x âˆ’ 3) with respect to x.

_{7}(2x âˆ’ 3) with respect to x.

**Solution:**

We have,

y = log

_{7}(2x âˆ’ 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 5xÂ° with respect to x.**

**Solution:**

We have,

y = tan 5xÂ°

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.

_{x}3 with respect to x.

**Solution:**

We have,

y = log

_{x}3As , 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.

^{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.

^{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

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