Welcome to your Differentiation(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Differentiate (x² - 1/x)² wrt x x³-3x²+2 2x²-2 4x³ -2/x³ -2 2/x³ +3x +2 None 2. Differentiate the function wrt x: x²+2 2-3x² 2(x - 1/x²) 1/x² None 3. Differentiate the functions wrt x:(x-2)(3x+5) 3x² 3x+2 4x+4 6x-1 None 4. Find the value of x at which the function y = x³ - 7x² + 15x has the greatest value 5 5/3 3/5 3 None 5. Find the minimum value of the function y = x³ + 3x² - 9x + 1 -4 -1 -3 -2 None 6. The radius of a spherical balloon is increasing at the rate of 0.25cm/s, find the rate at which the volume is increasing when its radius is 4cm 16π cm³/s 7π cm³/s 4π cm³/s 12π cm³/s None 7. Find, with respect to x, the derivative of sin x /(1- cos x) cos x -1 /(1- cosx) x 1 /(cosx -1) None 8. The side of a square of length 5 cm is increasing at 0.1m/s. What is the rate of increase of the area of the square? 4 cm² 1cm² 3cm² 2cm² None 9. Differentiate w.r.t x 7x4 - 5x 28x³-5 28x² -5x 14x 28+5x² None 10. Find the equation of the tangent to the curve y = 2x² - 5x + 1 at the point (2, -5) y = 4x + 12 x = 3y -11 y = 3x - 11 x = 4y - 2 None 11. The displacement xcm from a fixed point of a particle moving in a straight line after time t (s) is given by x = 12t - 15t² + 4t³. Find its acceleration in m/s², after 3s. 12 m/s2 42 m/s2 36 m/s2 72 m/s2 None 12. d/dx cos(3x² - 2x) is equal to sin(3x² - 2x) -6x+2cosx sin(3x² -(6x-2)sin(3x² - 2x) None 13. Iffind dy/dx (x-1)³ 1/(x+1)³ (x+1)³ 1/(x-1)³ None 14. Differentiate the function wrt x:(2x-7)² 28x² x+7x 8x-28 x²-14 None 15. A curve has equation y = x³ -4x² - 3x + 18, find dy/dx x² +12 x²-3x 8x+18 3x²-8x-3 None 16. Find the gradient of the curve y = 2√x - 1/x at the point x = 1 2 0 3 1 None 17. Differentiate w.r.t x sin³x -3sin²xcosx 3sin²xcosx -3cos²xsinx 3sin²x None 18. If loge(1/x)find dy/dx 1/x -x/2 x/2 -1/x None 19. Differentiate the function wrt x: 3x + 1/4x² 1/4x² 1/2 + 3x + 1/4x² 1/2 - 1/4x² None 20. The radius of a circle s increasing at the rate of 0.05 cm/s. Find the rate of increase of the circumference when the radius of the circle is 4 cm. 0.2π cm/s 4π cm/s 8π cm/s 10π cm/s None 21. Differentiate the function wrt x:y = √x 1/2√x x² √x 2√x None 22. Find dy/dx if : y = cos2xsinx + sin2xcosx -3cos2x cosx - 3sin2x sinx 3cos2x cosx - 3sin2x sinx -3cos2x cosx + 3sin2x sinx 3sin2x sinx None 23. Find the derivative of (2+3x)(1-x) with respect to x Choose File Drag and Drop File Here or Browse 24. Using the product rule differentiate wrt x(3x + 4)(x - 3) 6x-5 x²+12 6x² 9x-12 None 25. If y = sin²x, find the rate at which y changes with respect to x sinx cosx sinx + cosx 2cosx 2sinx cosx None 1 out of 25
