Differentiation(Senior Class Math Study by Topics) : GATE Academy

Welcome to your Differentiation(Senior Class Math Study by Topics)

NAME

PHONE NUMBER

1. Find the equation of the tangent to the curve

y = 2x² - 5x + 1
at the point (2, -5)

x = 3y -11

y = 4x + 12

y = 3x - 11

x = 4y - 2

2. Differentiate the functions wrt x:
(x-2)(3x+5)

4x+4

3x²

6x-1

3x+2

3. Given that V = 4/3 πr³ and
A = 4πr²,

find dA/dV

2/r

3/r

r/2

r/3

4. Differentiate (x² - 1/x)² wrt x

x³-3x²+2

2/x³ +3x +2

2x²-2

4x³ -2/x³ -2

5. Using the product rule differentiate wrt x
(3x + 4)(x - 3)

9x-12

x²+12

6x-5

6x²

6. If log_e(1/x)

find dy/dx

1/x

-1/x

-x/2

x/2

7. If y = sin²x,

find the rate at which y changes with respect to x

2sinx cosx

sinx cosx

2cosx

sinx + cosx

8. Differentiate the functions wrt x:
5(3x-4)²

60x+4x²

3x²+4

60x²

30(3x-4)

9. If y = 2xcos2x - sin2x, find dy/dx when x = π/4

-π

π/2

π/4

10. Differentiate the function wrt x:

1/2 + 3x + 1/4x²

3x + 1/4x²

1/2 - 1/4x²

1/4x²

11. What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?

6π cm³/s

2π cm³/s

8π cm³/s

4π cm³/s

12. Find the derivative of h(x) =

8x-8x-¹

3x-2

4x-¹

3-2x-¹

13. Find the minimum value of the function
2x³ - 6x²

-5

-8

14. Find the derivative of f(y) =

2y-4y-³

y-2

2-2yy³

15. Differentiate w.r.t θ

( sin θ / 3+ 2cos θ )

3cos θ + 2/(3 + 2cos θ )²

1/(3 + 2cos θ )²

3cos θ + 2/(3 + 2cos θ)

3cos θ + 2

16. d/dx cos(3x² - 2x) is equal to

sin(3x²

-6x+2cosx

sin(3x² - 2x)

-(6x-2)sin(3x² - 2x)

17. A body moves along x-axis and its position is given by x = 4.5t³ - 9t² -4t where x is in metres and t is in seconds. Find the velocity and acceleration at t = 2 s.

14 m/s and 18 m/s²

36 m/s and 14 m/s²

14 m/s and 36 m/s²

18 m/s and 14 m/s²

18. Find the gradient of the curve y = 2√x - 1/x at the point x = 1

19. Differentiate w.r.t x: x-4x³

1-12x²

1-4x²

1-4x

20. Determine the turning point of the curve

y = x² + 250/x

(5, 35)

(-5, 35)

(2, 7)

(-2, 7)

21. Find the value of x at which the function

y = x³ - 7x² + 15x has the greatest value

3/5

5/3

22. Find the derivative of

y = 2 t^{4} - 10 t^{2} + 13 t

2t⁴- 10t² + 13t

20t + 14

20t

4t³-5

8t³ -20t + 13

23. Differentiate the function wrt x:

2-3x²

x²+2

2(x - 1/x²)

1/x²

24. A curve has equation y = x³ -4x² - 3x + 18, the point P(-2, 0) lies on the curve. Find the gradient of the tangent to the curve at P.

25. At what rate in cm² per cm is the area of the circle changing w.r.t its radius when the radius is 5cm?

3πcm²/cm

5πcm²/cm

20πcm²/cm

10πcm²/cm

26 out of 25

Differentiation(Senior Class Math Study by Topics)

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