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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 2Differentiate 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  

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[-ex tanx].
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.\[f(x)=\left\{\begin{matrix} \frac{kcosx}{\pi -2x}\; \; ,\; \; x<\frac{\pi }{2}\\\\\frac{3tan2x}{2x-\pi }\; \; ,\; \; x>\frac{\pi }{2} \end{matrix}\right.\; \; \; \; \; \; \; \: \: \: ....\: \: Ans\: \: k=6\]
Question 23. 
 Find the value of k for which the following function is continuous at x = 0\[f(x)=\left\{\begin{matrix} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}\; \; ,\; \; -1\leq x<0\\\\ \frac{2x+1}{x-2}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \:, \: \: \: \: \: \: 0\leq x<1 \end{matrix}\right.\: \: \: \: \: .....\: \: \: \: \: \: Ans\: k=-\frac{1}{2}\]
Question 24: 
Show that f(x) = |x - 2| is continuous but not differentiable at x = 3.

Question 25: 
Discuss the continuity and differentiability of the following function. \[f(x)=\left\{\begin{matrix} 1-x\: \:\: \: \: \: \: \: ,\: \: x<1\\(1-x)(2-x),\: 1\leq x\leq 2 \\ 3-x\: \: \: \: \: ,\: \: \: \: \: x>2 \end{matrix}\right.\]
Answer 26: 
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 27
Check the differentiability of the function

equation  
Solution Hint

equation 

equation 

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

Question 28

If f(x) = (x + 1)cosx  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



THANKS FOR YOUR VISIT
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Comments

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

    ReplyDelete

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