Welcome to your Differentiation(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Differentiate the function wrt x:y = √x x² 2√x √x 1/2√x None 2. 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. 21 29 25 22 None 3. Differentiate the function w.r.t x: y= 5(x+5) 25 5 5x 25x² None 4. The length of each of a metal cube increases at the rate of 0.025cm²s-¹ when heated. Find the rate of increase in cm²s-¹ of the total surface area of the cube, when the length of each side is 6cm 1.8 1.6 1.0 1.5 None 5. Find the minimum value of the function y = x³ + 3x² - 9x + 1 -1 -4 -3 -2 None 6. Using the product rule differentiate wrt x(3x + 4)(x - 3) 9x-12 x²+12 6x² 6x-5 None 7. If y = x³ + 3x², find 2(dy/dy) - x(d²y/dx²) 4x 2x 6x 5x None 8. Find the derivative of f(y) = 2-2yy³ y-2 2y-4y-³ 4y None 9. The distance s metres travelled by a particle in time t seconds is given by s = 12 + 40t - 2t². Find the distance travelled by the particle before coming to rest. 212m 180m 200m 120m None 10. Find the maximum value of the function 3x²-x³ 1/2 -3 -2 4 None 11. 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 3cm² 1cm² 2cm² None 12. If y = 2x², find the appropriate increase in y when x increases from 5 to 5.01 6 0.4 0.3 0.2 None 13. Differentiate sinx - xcosx sinx + cosx cosx + xsinx xcosx xsinx None 14. Find the minimum value of the function3x²-x³ 0 -1 1 2 None 15. Differentiate the function wrt x(x+3)³ x²+3 x+3x² 3(x+3)² x²+9 None 16. If y = 8x² - 5x, find the approximate change in y if x changes from 1 to 1.05. 0.55 0.25 1.5 1.0 None 17. The distance s metres after time t second covered by a particle moving along a straight line is given by s = t³ - t² - t - 2Find the average acceleration between t = 2 and t = 4 4ms-² 2ms-² 6ms-² 3ms-² None 18. Find the maximum and minimum values of thefunction 3x² - x³ max = 4, min = 0 max =-2, min = -6 max = 10, min = 4 max = 1, min = -1 None 19. Find the derivative of <span class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #000000;font-family: Helvetica, Arial, Verdana, sans-serif;background-color: #ffffff" role="presentation" data-mathml="y=2t4−10t2+13t"><span class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #000000;font-family: Helvetica, Arial, Verdana, sans-serif;background-color: #ffffff" role="presentation" data-mathml="y=2t4−10t2+13t">y = 2t4- 10t² + 13t 20t 4t³-5 20t + 14 8t³ -20t + 13 None 20. Differentiate w.r.t x cos³x 3cos²xsinx -3cos²xsinx -3cos²x 3sinx None 21. If x³ + y³+ 6xy = 0, find dy/dx by implicit differentiation - (2y + x²)/(2x + y²) x/(2x + y²) (2y + x²)/ (2x + y²) - (2y + x²)/ y None 22. The speed s of a particle after t seconds is given by v = 7 + 25t -4t² . Find the acceleration of the particle after 2 seconds. 28 m/s² 25 m/s² 9 m/s² 41 m/s² None 23. From the curve y =(4 - x)(3 + x), find the gradients of the curve at the points P(-1, 10) and Q(3, 6) mp = 3, mq = -5 mp = 3, mq = -6 mp = -3, mq = 4 mp = -4, mq = 4 None 24. Find the gradient of the curve y = 2√x - 1/x at the point x = 1 3 2 0 1 None 25. Differentiate the functions wrt x:(x-2)(3x+5) 3x² 3x+2 6x-1 4x+4 None 1 out of 25