**Math Assignment Class XII Chapter 5 Derivatives**

** Question 1 Use chain rule to find the derivative of **** **

**Question 2. Differentiate the following w.r.t. x **

**Answer**

** Solution Hint **

** Now differentiating w. r. t. x and taking log10 as constant.**

Question 3. Differentiate the following w. r. t. x at x = 1

**Answer: 2e**

**Question 4. **

** , Then prove that : ****Question 5: Differentiate log(x e**^{x}) w. r. t. xlogx.

**Answer 5: **

**Question 6: Differentiate x**^{2} w. r. t. x^{3}. ........... Ans:
2/3x.

**Question 7: , Prove that **

**Solution Hint: **

**Dividing on both side by **

** ****Now differentiating w. r. t. x we get the required answer. **

**Question 8: Differentiate (x**^{x})^{x } w. r. t. x

**Answer **

**Solution Hint: **

** Now differentiating w. r. t. x**

**Question9. Differentiate
x**^{16}y^{9 }= (x^{2 }+ y)^{17} w. r. t. x ,

**Answer : ****Question10) Differentiate (logx)**^{x} + x^{logx}, w. r.
t. x.

**Answer **

**Question11**

**Answer: ****Question 12: **

**Then prove that : **

**Solution 12:**

**Differentiating both side w. r. t. x we get **

**Question 13. Find dy/dx at x = 1, y = Ï€/4, If Sin2y + cosxy = k**

**Answer 13. **

**Question 14. If x = a(2Î¸ - sin2Î¸) and y = a(1-cos2Î¸), find dy/dx, when Î¸ = Ï€/4. **

Answer 14: [ 1]

Question 15. Differentiate Log(cosex) w. r. t x

**Ans[-ex tanx].**

Question 16.

** then prove that**

Question 17. ** then prove that **

**Question 18. **

** , then find the value of **** **

Question 19: Differentiate the following w. r. t. x

**Ans: **

**Question 20. Differentiate the following w. r. t. x **

** Ans: ****Question 21. Differentiate: ****Ans: ****Question 22. **

**Find the value of k if the following function is continuous.**

**Answer: k = 6**

**Question 23. **

** Find the value of k for which the following function is continuous at x = 0**

**Answer: k = -1/2**

Question 24:

**Show that f(x) = |x - 2| is continuous but not differentiable at x = 2.**

**Question 25: **

**Discuss the continuity and differentiability of the following function. **

**Answer:**

**f(x) is continuous at x = 1 but not continuous at x = 2**

f(x) is differentiable at x = 1.

As f(x) is not continuous at x = 2 so f(x) is not differentiable at x = 2.

**Question 26**

**Check the differentiability of the function**

**Solution Hint**

** **

**LHD = RHD ⇒ f(x) is differentiable at x = 2**

**Question 27**

**Question ****Check the
differentiability of **

** ****Solution Hint:**

**At x = 2, LHD = 2 and RHD = -1**

**As LHD ≠ RHD, this function is not differentiable**

**Question 28**

**If f(x) = (x + 1)**^{cotx} is continuous at x = 0 then find f(0).

**Answer = e**

**Solution: We know that **

** ****Now, f(x) = (x+1)**^{cotx}

**Log[f(x)] = Log[(x+1)**^{cotx} ]

**Log[f(x)] = cotx Log(x+1)**

**Question 29 : Find ****Solution: **

**Question 30 :****Check whether the function f(x) = x**^{2} |x| is
differentiable at x = 0 or not.

**Solution Hint **

**This function can be written as **

**Find LHD and RHD we get**

**LHD = RHD = 0**

**Yest this function is differentiable.**

**Question 31 :****If , then find dy/dx**

**Answer: **

**Question 33 :****If then prove that **

**Solution Hint for the Q. No. 33 to Q. No. 40 **

**Question 34 :****If y = cosec(cot**^{-1}x), then prove that

** **

**Question 35 :****If x = e**^{cos3t} and y = e^{sin3t} , prove that

**Question 36 :****If x = e**^{x/y},
then prove that ** **

**Question 37:****If
y = cos**^{3}(sec^{2}2t), find dy/dt

**Question 38****If x**^{y} = e^{x - y}, prove that

**Question 39****Given
that y = (sinx)**^{x} . x^{sinx} + a^{x}, find dy/dx

**Question 40**

**If x = a
sin**^{3}Î¸, y = bcos^{3}Î¸, then find at Î¸ = Ï€/4

**THANKS FOR YOUR VISIT**

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