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### Math Assignment Class XI Ch -12 | Derivatives

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## Math Assignment Class XI Ch - 12

**Extra questions of chapter 12 Limits & Derivatives class 11 with answers and hints to the difficult questions, strictly according to the CBSE and DAV syllabus. Important and useful math. assignment for the students of class 11**

**MATHEMATICS ASSIGNMENT ON **

**DERIVATIVES (XI)**

**Strictly according to the CBSE and DAV Board**

**Question 1: Differentiate the following by first principal**

**(i) sin 2x (ii) ****x e ^{x}**

**(iii)**

**x**

^{2}e^{x}**(iv)**

**Cos**

^{2}x**(v) x**

^{2}cosx**Question 2 : Using first principle find the derivative of x sinx**

**Ans: x cosx + sinx**

**Question 3 : Find the derivative of sin**

^{2}x w.r.t. x, by first principle.**Ans: 2sinxcosx = sin2x**

**Question 4 : Using first principle find the derivative of sin (x**

^{2}+ 1).**Ans: 2x cos (x ^{2} + 1)**

**Question 5 : Find the derivative of cos(5x + 2) w.r.t x by first principle.****Ans: - 5sin(5x + 2**

**Question 6 : Find the derivative of tan(2x + 3) w.r.t. x, by first principle**

**Ans: 2sec ^{2}(2x + 3)**

**Question 7 : Find the derivative of tan (ax + b) from the first principle.**

**Ans: asec ^{2}(ax + b)**

**Question 8 : Find the derivative of f(x) = from first principle.**

**Ans: **

**Question 9 : Find the derivative of f(x) = from first principle.**

**Ans: **

**Question 10 : Find the derivative of using first principal**

**Ans:**

**Question 11 : Find the derivative of f(x) = with respect to x using first principal.**

**Ans: **

**Solution hint for this question is given at the end.**

**Question 12 : Differentiate :**

**Ans : **

**Question 13 : Differentiate:**

**Ans : a ^{x }Loga + ax^{a-1}.**

**Question 14 : Differentiate:**

**Ans : cosx**

**Question 15 : Differentiate:**

**Ans : 3x ^{2}tanx + x^{3}sec^{2}x**

**Question 16 : Differentiate:**

**Ans : 2x sinx logx + x ^{2} cosx logx + x sinx **

**Question 17 : Differentiate:**

**Ans : x ^{4}e^{x} (5 + x) + x^{5}(6logx + 1)**

**Question 18 : Differentiate:**

**Ans :**

**Question 19 : Differentiate:**

**Ans:**

**Question 20 : Differentiate:**

**Ans: cosa.sec2x**

**Question 21 : If y = xsinx + cosx then find at x =**

**Ans: 0**

**Question 22 : Find the derivative of cosx - sinx at x =**

**Ans: **

**Question 23 : Find the derivative of w.r.t x**

**Ans: **

**Question 24 : Find the derivative of f (x) = w. r. t. x**

**Ans: **

**Question 25 : Differentiate:**

**Question 26 : Differentiate:**

**Question 27 : Differentiate:**

**Question 28 :**Differentiate : y = with respect to x

**Question 29 :**If , then find at x = 0

^{o }

**Question 30 :**If , then prove that

**Question 31 :**

^{2}-5x +4 and f’(3) = 37, find the value of k.

******************************************

**SOLUTION HINT**

*****************************************

Formula to find the derivative by using first principal

**Solution Hint Q11**

**Now by definition of first principle, we have**

**Applying CD formula here, we get**

**Putting the limit in the first cos function we get**

**Rationalizing the numerator of the angle of sine function, we get**

**Simplify the above equation we get**

**Now making the denominator similar to the angle of the sine function, we get**

**Taking limit and applying the formula , we get**

**THANKS FOR YOUR VISIT**

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