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Math Assignment Class XI Ch -13 | Derivatives
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Math Assignment Class XI Ch - 13
DERIVATIVES
Extra questions of chapter 13 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 ex (iii) x2ex (iv) Cos2x (v) x2cosx
Question 2 : Using first principle find the derivative of x sinx
Ans: x cosx + sinx
Question 3 : Find the derivative of sin2x w.r.t. x, by first principle.
Ans: 2sinxcosx = sin2x
Question 4 : Using first principle find the derivative of sin (x2 + 1).
Ans: 2x cos (x2 + 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: 2sec2(2x + 3)
Question 7 : Find the derivative of tan (ax + b) from the first principle.
Ans: asec2(ax + b)
Question 8 : Find the derivative of f(x) =
Ans:
Question 9 : Find the derivative of f(x) =
Ans:
Ans:
Question 11 : Find the derivative of f(x) =
with respect to x using first principal.
Ans:
Question 12 : Differentiate :
Ans :
Question 13 : Differentiate:
Ans : ax Loga + axn-1.
Question 14 : Differentiate:
Ans : cosx
Question 15 : Differentiate:
Ans : 3x2tanx + x3sec2x
Question 16 : Differentiate:
Ans : 2x sinx logx + x2 cosx logx + x sinx
Question 17 : Differentiate:
Ans : x4ex (5 + x) + x5(6logx + 1)
Question 18 : Differentiate:
Ans :
Question 19 : Differentiate: 
Ans:
Question 20 : Differentiate: }{cosx})
Ans: cosa.sec2x
Question 21 : If y = xsinx + cosx then find
Ans: 0
Question 22 : Find the derivative of cosx - sinx at x =
Ans:
Question 23 : Find the derivative of
Ans:
Question 24 : Find the derivative of f (x) =
Ans:
Question 25 : Differentiate:
Question 26 : Differentiate:
Question 27 : Differentiate:
Question 28 : Differentiate : y =
******************************************
SOLUTION HINT
*****************************************
Formula to find the derivative by using first principal
Product Rule to find the derivative
Quotient rule to find the derivative
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
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