Question # 1

The derivative of√x at x =a is:

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1/2a

2 / √a

2√x

1 / 2√x

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zero at x

differentiable at x

continuous at x

none of these

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If y=x^mthen dy/dx equals:

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mx

x/m

mx^m-1

xm^m-1

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-2x

x^-3

-2x³

if x∈ D∱ and∱¹^{(x) exists, then}∱ is said to be

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zero at x

Differentiable at x

Continuous at x

None of these

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d/dx (cos x²) =

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-2x cos x

-2x sin x²

-2x tan x

-2x sec² x

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Differentiation of sin x w.r.t. cot x is:

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-sin² x sec x

-cos x sin² x

-cos² x tan x

-sin² x

d/dx [tan² x]

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2tan x sec² x

2tan x sec x

2 cot x tan x

2sec² x cos² x

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2x

x/2

2x³

x³/2

If c is a constant, then d/dx (c) =

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0

c

cx

1

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If y = xⁿthen dy/dx equals:

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nx

x^n-1

nx^n-1

n

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x²+ 2

3x + 2

3x²+ 5

3x²+ 2

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0

8

5

9

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If x =1 -t² and y =3t²- 2t³ then dy/dx =

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(1-t)

3(1+t)

3(t-1)

3/1-t

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8

1/8

1/3

2/3

d/dx(x³ + 2x +3)=

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x²+ 2

3x + 2

3x²+ 5

3x2 + 2

If 3x + 4y +7 = 0 , then dy / dx =

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-1/2

-4/3

7/2

-3/4

The derivative of 1/x^m is:

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x^m+1/ m

m(x)^m-1

(m-1) x^-m

m/x^m+1

∱(x) = ax²-3x -5, and∱¹(2) = 9, a is equal to

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2

3

-2

4

Let∫ be real valued function continuous in the interval (x,x₁)⊆ D∫ (the domain of∫),

then∱(x₁) -∱ (x)/x₁-x represents:

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Instantaneous rate

Average rate of change

Differential coefficient

None of these

d/dx (cosec x)

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-sec x tan x

sin x cos x

-csc x cot x

2sin x cos x

If∱(x) = 1/x-2 then∱¹(0) equals:

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-1/4

-3/2

-1/2

1/5

d/dx (cos x sin x) =

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cos² x - sin² x

2cos²x + sin² x

2cos² x - sin² x

1 - sin²x

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