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Home/ECAT/ECAT Mathematics Differentiation Online Test

ECAT Mathematics Differentiation Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Differentiation

ECAT Math Differentiation Chapter Online Test

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

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Page 1 of 2

1. 2√tanx d/dx √tanx =

√tanx

0

Sec² x

1/2√tanx sec² x

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2. If f(x) = sec⁻¹ x, then f’ (cosh x) =

2 cosech 2x

2 sech 2x

2cosh 2x

2 sinh 2x

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3. If S = 980t – 490t², the velocity at time t = 2 is

490m/sec

None of these

1960m/sec²

-490m/sec

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4. d/dx √sec2x = ?

1/2√sec2x sec 2x. tan 2x

None of these

sec 2x. tan 2x/√sec2x

√sec2x

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5. d/dx (axᵐ+bxⁿ) =

amxᵐ⁻¹+bnxⁿ⁻¹

axᵐ⁻¹+bxⁿ⁻¹

mxᵐ⁻¹+nxⁿ⁻¹

xᵐ⁻¹+xⁿ⁻¹

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6. 3x + 4y + 7 = 0 ⇒ dy/dx =

- 4/3

- ¾

0

¾

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7. d/dx (cos⁻¹ 3x) = ?

-3/x⁴

-5/x⁴

-6/x⁴

4/x⁴

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8. If f(x) = tan √π, the f’ (π²) =

√π

2π

1/2π

π

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9.

D

C

A

B

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10. 1/3x² d/dx (tan x³) = ?

3 sec² x

3x² sec² x³

sec² x

sec² x³

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11. d/dx In (In(In x)) = ?

1/x In x

1/x In a

1/x

1/x, 1/Inx, 1/In(In x)

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12. d/dx (x³ + 2) =

x³

3

3x

3x²

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13. In case of strictly decreasing function, the derivative is

Negative

Zero

Positive

Either negative or zero

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14. If f(x) = 3 – √x, then f’(1) =

- ½

1

½

0

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15.

D

A

C

B

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16.

A

D

C

B

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17. The derivative of an even function is always

Does not exist

Odd function

Both a and b

Even function

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18.

A

D

B

C

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19. If y/x = tan⁻¹ x/y, then dy/dx = ?

1/xy

y/x

x/y

xy

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20. d/dx [In f(x)] =

1/f(x)

f’(x)/f(x)

1/x

f(x)f’(x)

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21. d/dx [1/(3x + 2)³] =

-9/(3x + 2)⁴

9(3x + 2)⁻⁴

3/(3x + 2)²

9/(3x + 2)²

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22. If f(x) = cosx, then f’ (cox⁻¹ 3x) =

3/√1 – 9x²

Cosx

3x

- 3/√1 – 9x²

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23.

C

D

A

B

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24.

B

C

A

D

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25. f(x) - x¹⁰⁰ ⇒ f’ (1) =

0

50

100

99

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26. d/dx [f(x)/g(x)] =

f’(x)g’ (x) – f’(x)g’(x)/[g(x)² =

f’(x)/g’(x)

f’(x)g (x) + f (x)g’(x)/[g(x)² =

f(x)g’(x) – f’(x)g(x)/[g(x)² =

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27. d/dx [5f(x)] =

5 + f’(x)

5f’(x)

5

f’(x)

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28. dy/dx = ? if x = a(1 – t²)/2at, y = 2bt/1+t²

2at/t²(t – 1)

a(t² – 1)/2bt

b(1 – t²)/2at

None of these

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29.

A

C

D

B

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30.

C

A

D

B

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31. If y = cos ax then y₈₋₇

a⁸ cos (ax + 4π)

a⁸ cos (ax + 5π)

a⁸ cos (ax + 3π)

a⁸ cos (ax + 2π)

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32. f(√x) = sin x ⇒ f’ √π =

2√π cos √π

-2√π

2π cos π²

2π cos √π)

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33. d/dx [f(x) – g(x)] =

f’(x) g’(x)

0

f’(x) – g’(x)

f’(x) + g’(x)

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34. x³ d/dx (In 2x) = ?

x²

2x²

3x²

6x²

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35. The point at which curve y=x² - 4x + 6 has gradient -2 is

(0, 1)

(1, 0)

(-3, 2)

(2, 1)

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36. d/dx = (secx) =

secx tan x

-cosx

sec²x

-sinx

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37. d/dx(xⁿ – 2) =

(n – 2)xⁿ⁻¹

(n – 1)xⁿ⁻¹

nx⁻

x(xⁿ⁻¹ – 2)

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38. d/dx (ax + b)ⁿ

n(ax + b)ⁿ⁻¹

naxⁿ⁻¹

na(ax + b)ⁿ⁻¹

n(axⁿ⁻¹ + b)

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39. If f(x) = sin x, then fᵐ (0) = ?

0.5

1

-1

0

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40. If y = 7x⁶+3x⁴-5x³+2 then which one is true

Y₆ = 0

Y₈ = 0

Y₅ = 0

Y₇ = 0

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41. If f(x) = 3 + x then

f’ (0) < f’ (1)

f’ (0) = f’ (1)

f’ (0) ≠ f’ (1)

f’ (0) > f’ (1)

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42. (1 + x²) d/dx = (tan⁻¹ x – cot⁻¹ x) =

-1

1

0

2

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43. The maximum value of function f(x) = sin x cos x is

2

None of these

1

½

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44. d/dx = tan 3x =

3sec + 3x

sec² 3x

sec² x

3sec² x

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45. x d/dx (In x) =

In x

0

X

1

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46. f(x) = 3x2 – 2x + 1 ⇒ f’(0) =

2

5

-2

1

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47. Differentiate x⁹ w.r.t x², we get

5x⁹

5/2 x⁶

9/2 x⁷

3x⁶

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48. d/dx [f(x) + g(x) + h(x)] =

f’(x) – g’(x) + h’(x)

f’(x) + g’(x) + h’(x)

f’(x) – g’(x) – h’(x)

f’(x) + g’(x) – h’(x)

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49.

A

C

B

D

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50. y = xtan x/2, then (1+cosx) dy/dx – sin x =

0

x

xy

y

Loading...

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Danial MalikLast Updated: April 18, 2025

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