Question # 1

d/dx (cos x²) =

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-2x cos x

-2x sin x²

-2x tan x

-2x sec² x

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x²+ 2

3x + 2

3x²+ 5

3x²+ 2

d/dx(x³ + 2x +3)=

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x²+ 2

3x + 2

3x²+ 5

3x2 + 2

If f(x) = c then∱¹(x) equals:

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1

0

cx

c

d / dx (cot x) =

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Sec x tan x

-csc² x

Sec² x

1/cot² x

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d/dx (cos x sin x) =

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cos² x - sin² x

2cos²x + sin² x

2cos² x - sin² x

1 - sin²x

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

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2

3

-2

4

If y = xⁿthen dy/dx equals:

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nx

x^n-1

nx^n-1

n

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If∱(x) = 2x³ + 1 then∱¹(0) =

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0

1

6

None of these

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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2x

x/2

2x³

x³/2

If y = 3 x + 2cos x, then dy/dx =

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3-2 sin x

3-t sin x

3x² - 2sin x

3(1-4 sin x)

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If∱(x) = 1/x-2 then∱¹(0) equals:

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-1/4

-3/2

-1/2

1/5

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

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0

8

5

9

If x² + y² = 1, then dy/dx

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y/x

-x/y

1/x

None of these

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

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-1/2

-4/3

7/2

-3/4

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

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0

8

5

9

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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

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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Mathematics ECAT Pre Engineering Chapter 18 Basic Concepts & Definitions Online Test MCQs With Answers

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