Welcome to your Differentiation(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. If y = 3cos4x, find dy/dx 12cos4x -12sin4x -12cos4x 12sin4x 2. Differentiate the function w.r.t x: y = 4(x² - 3) 8x 8x² x²-3 6x 3. Differentiate, with the respect to x: cosx - x sinx -2sinx + xcosx -2sinx - xcosx 2sinx -xcosx xcosx 4. Differentiate the function wrt x:7x + √x³ 7 + 3√x/2 7√x x³ 4 + √x 5. Iffind dy/dx (x+1)³ (x-1)³ 1/(x+1)³ 1/(x-1)³ 6. Find the slope of the tangent to the curve y = 3x² - 2x + 5 at the point (-1, 10) 8 4 -8 -4 7. Find the equation of the tangent to the curve y = 2x² - 5x + 1 at the point (2, -5) y = 3x - 11 x = 4y - 2 x = 3y -11 y = 4x + 12 8. Differentiate x/cosx wrt x cosecx tanx + cosecx sinxcosx secx + xsecxtanx 9. Differentiate the function w.r.t x: y= 5(x+5) 5x 5 25 25x² 10. Find the differential coefficient ofat the point (1, -1) 3 5/2 2/5 1/3 11. A ball is thrown vertically upwards and its height s metres after t seconds is given by s = 16t - 4t². Find the time when the velocity is 8 m/s. 1s 4s 2s 3s 12. If the radius of the base of a cone is decreasing at 2 cm/s, find the rate of increase in volume when the radius of the base is 5 cm. 50π cm³/s 20.5π cm³/s 25π cm³/s 10π cm³/s 13. A rectangular goat pen is to be fenced off near the brick wall. The total length of the fence is 20m. What must be the length of the side parallel to the brick wall to yield the greatest area? 8 m 16m 10 m 12 m 14. Find the derivative of (2+3x)(1-x) with respect to x 15. Differentiate (x² - 1/x)² wrt x 2x²-2 x³-3x²+2 4x³ -2/x³ -2 2/x³ +3x +2 16. Differentiate w.r.t x sin³x -3cos²xsinx 3sin²x -3sin²xcosx 3sin²xcosx 17. 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. 72 m/s2 36 m/s2 42 m/s2 12 m/s2 18. If y = x³ + 3x², find 2dy/dx - x d²y/dx² 6 4 6x 6x² 19. Find dy/dx if y = logetan2x 2cot²xsecx 2sec²2x 2cot2xsec²2x 2cot2x 20. Find the differential coefficient of y = -5/(x²+4) at the point (1, -1) 5/2 -5/2 2/5 -2/5 21. Differentiate w.r.t x cos³x 3cos²xsinx -3cos²xsinx -3cos²x 3sinx 22. Find, from the first principles, the derivative with respect to x of the function y = 2x² - x + 3 4x - 4 4x - 2 4x 4x - 1 23. Find the minimum value of the function y = x³ + 3x² - 9x + 1 -4 -1 -3 -2 24. Find, w.r.t.x, the derivative of (2x² - x + 3)³ 2(2x+3) 3(4x-1) 7(2x² - x + 3)³ 3(4x-1)(2x² - x + 3)³ 25. Differentiate w.r.t x 5x³ 15x 5x 15x² 5x² 1 out of 25