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Derivative Functions:

The derivative function is used to differentiate the given function at all the points in the domain of the function where the derivative exists.


It is calculated by the formula f’(x) = Derivative Functions Formula

 

Derivative Functions Sample Questions:

Question 1: Find the derivative of a function f(x) = x^2 + 2x +4

 

(a) x

(b) 2x+1

(c) 2(x+1)

(d) x+1


Answer: (b)

Explanation: f'’(x) = Explanation 1

 

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Question 2: The position of particle is along s(t) = 4t^2-2t+7, find the velocity of the particle

 

(a) 4t+2 

(b) 8t – 2

(c) 4t -2

(d) 4(2t - 2)


Answer: (a)

Explanation: s(t) = 4t^2-2t+7

 

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Question 3: Find the slope of the curve 4x^2 +4= 3+f(x) at x = 1

 

(a) 16

(b) 15

(c) -3

(d) 8


Answer: (d)

Explanation: f'’(x) = Explanation 3

 

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Question 4: Check the differentiation of  x sinQuestion 4 at x =0

 

(a) 0

(b) Infinite

(c) 1

(d) Does Not Exist


Answer: (d)

Explanation: Limit does not exist hence the function is not differentiated at x =0

 

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Question 5: f(x) = 3x^2-4x+6 find f’’(x)

 

(a) 3

(b) -3

(c) 6

(d) -6


Answer: (c)

Explanation: f(x) = 3x^2-4x+6,    f(x+h) = 3(x+h)^2 -4(x+h) +6

 

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Question 6: Find the differentiation of y = Question 6

 

(a) 2a (ax+b)^

(b) na (ax+b)^n-i  

(c) na (ax+b)^

(d) n(ax+b)^n-i


Answer: (b)

Explanation: Explanation 6

 

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Question 7: If f(x) =  tan Question 7, then f’(Question 7.1)=

 

(a) Question 7 a

(b) Question 7 b

(c) Question 7 c

(d) Question 7 d


Answer: (a)

Explanation:  f(x) = tanExplanation 7

 

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Question 8: Question 8 =

 

(a) 2xcosx^2

(b) cosx^2

(c) 2xcos^2x 

(d) 2cosx^2


Answer: (d)

Explanation: Explanation 8 = Explanation 8.1 2x

 

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Question 9: f(x) =  tan^-1x, f (cotx)=

 

(a) Question 9 a

(b) sin^2x

(c) cos^2x

(d) sec^2x


Answer: (b)

Explanation: f(x) = tan^-1x

 

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Question 10: The derivative of natural exponential function can be found by using

 

(a) Implicit functions

(b) Using byparts law 

(c) Limit of differentiation

(d) Simple differentiation


Answer: (c)

Explanation: Explanation 10 f(x) = Explanation10.1 (using the limit of differentiation)

 

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