Question # 1

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

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0

c

cx

1

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If∱(x) = c then∱^{1 (x0 equals:}

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1

0

cx

c

If ∱(x) = x^2/3then∱¹(x) at x = 8 equals:

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8

1/8

1/3

2/3

d / dx (cot x) =

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Sec x tan x

-csc² x

Sec² x

1/cot² x

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If x² + y² = 1, then dy/dx

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y/x

-x/y

1/x

None of these

If x = at² and y = 2at then dy/dx =

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2a/y

y/2a

-a/2y

-2y/a

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

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8

1/8

1/3

2/3

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mx

x/m

mx^m-1

xm^m-1

If y = 1/x²then dy/dx equals:

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-2x

x^-3

-2/x³

-2x³

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0

8

5

9

If∱(x) = x⁵ + x³ + x the value of∱¹(1) is:

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0

8

5

9

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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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

If f(x) = c then∱¹(x) equals:

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1

0

cx

c

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2x

x/2

2x³

x³/2

d/dx (cos x²) =

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-2x cos x

-2x sin x²

-2x tan x

-2x sec² x

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If∱(x) = x^-100the value of∱¹(1) is:

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100

-100

0

-101

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100

-100

0

-101

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zero at x

differentiable at x

continuous at x

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

The derivative of√x at x =a is:

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1/2a

2 / √a

2√x

1 / 2√x

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

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