Featured Posts

Math Assignment Class XII Ch-5 | Derivatives

Math Assignment Class XII Chapter 5 Derivatives

 Question 1 Use chain rule to find the derivative of 

equation 

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

equation  

Answer

equation

 Solution Hint  

equation

equation

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

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

equation 
Answer: 2e
Question 4

equation ,  Then prove that :   equation
Question 5: Differentiate log(x ex)  w. r. t.   xlogx. 

Answer 5:   equation

Question 6: Differentiate x2 w. r. t. x3.        ...........    Ans:  2/3x.

Question 7equation, Prove that   equation 

Solution Hint: 

 equation  
Dividing on both side by   equation

equation

equation 
Now differentiating w. r. t. x we get the required answer. 
Question 8: Differentiate  (xx) w. r. t. x  
Answer 
equation 
Solution Hint: 
equation  Now differentiating w. r. t. x
Question9.   Differentiate x16y9 = (x2 + y)17 w. r. t. x ,
Answer :    equation
Question10) Differentiate  (logx)x + xlogx, w. r. t. x. 
Answer  
equation

Question11
equation
Answer: equation 
Question 12
equation 
Then prove that :   equation

Solution 12:

equation

equation

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

equation

Question 13. Find dy/dx at x = 1, y = π/4, If Sin2y + cosxy = k
Answer 13.  equation

Question 14. If x = a(2θ - sin2θ) and y = a(1-cos2θ), find dy/dx, when θ = π/4.
Answer 14: [ 1]
Question 15. Differentiate Log(cosex) w. r. t x 
Ans[ -cotx ].
Question 16.
equation  then prove that

equation
Question 17. 
equation  then prove that   equation

Question 18. 
equation , then find the value of   equation 
 
Question 19: Differentiate the following w. r. t. x

equation  
Ans:  equation

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

equation     Ans:   equation
Question 21. Differentiate:  equation 
Ans:  equation
Question 22. 
Find the value of k if the following function is continuous.
equation 
Answer: k = 6
Question 23. 
 Find the value of k for which the following function is continuous at x = 0
equation 
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. 
equation
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

equation  
Solution Hint

equation 

equation 

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

Question 27
Question Check the differentiability of 
equation 
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 

equation 
Now, f(x) = (x+1)cotx  

Log[f(x)] = Log[(x+1)cotx ]

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

equation 

equation 

equation 
equation 
equation 

Question 29 :  Find   equation 
Solution:  equation  
equation 

Question 30 :

Check whether the function f(x) = x2 |x| is differentiable at x = 0 or not.

Solution Hint 

This function can be written as  equation 

Find LHD and RHD we get

LHD = RHD = 0

Yest this function is differentiable.

Question 31 :

If  equation , then find dy/dx

Answer:  equation  

Question 33 :

If  equation  then prove that   equation  

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

Question 34 :

If  y = cosec(cot-1x), then prove that 

equation 

Question 35 :

If x = ecos3t  and y = esin3t  , prove that   equation  

Question 36 :

If x = ex/y, then prove that  equation  

Question 37:

If y = cos3(sec22t), find dy/dt

Question 38

If xy = ex - y, prove that  equation 

Question 39

Given that y = (sinx)x . xsinx + ax, find dy/dx  

Question 40

If x = a sin3θ, y = bcos3θ, then find equation   at Î¸ = Ï€/4


THANKS FOR YOUR VISIT
PLEASE COMMENT BELOW

Comments

  1. Good and better also
    Mujhe bohot help hua hai isse
    Thz for help

    ReplyDelete

Post a Comment


Breaking News

Popular Post on this Blog

Theorems on Quadrilaterals Ch-8 Class-IX

Lesson Plan Maths Class 10 | For Mathematics Teacher

Mathematics Lab Manual Class XII | 14 Activities

SUBSCRIBE FOR NEW POSTS

Followers