02/04/2020 Differentiation(Senior Class Math Study by Topics) 0Comments by Gate Academy Welcome to your Differentiation(Senior Class Math Study by Topics) NAME EMAIL PHONE NUMBER 1. Differentiate sinx - xcosxxcosxsinx + cosxxsinxcosx + xsinx2. Given that V = 4/3 πr³ and A = 4πr², find dA/dVr/3r/22/r3/r3. Find dy/dx if y = logetan2x2cot2x2sec²2x2cot2xsec²2x2cot²xsecx4. Differentiate w.r.t x sin³x-3cos²xsinx3sin²x3sin²xcosx-3sin²xcosx5. Find the derivative of f(y) =y-24y2-2yy³2y-4y-³6. If y = 2xcos2x - sin2x, find dy/dx when x = π/4ππ/4-ππ/27. What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?6π cm³/s4π cm³/s8π cm³/s2π cm³/s8. 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 = -6mp = -3, mq = 4mp = -4, mq = 4mp = 3, mq = -59. Use the product rule to differentiate wrt xx³(2x+5)³4x+510x(2x+5)²3x²(4x+5)(2x+5)²2x+2010. Find, from the first principles, the derivative with respect to x of the function y = 2x² - x + 34x4x - 24x - 44x - 111. Differentiate the function wrt x(x+3)³x²+3x²+9x+3x²3(x+3)²12. 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/s²14 m/s and 36 m/s²18 m/s and 14 m/s²36 m/s and 14 m/s²13. 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?3cm²1cm²2cm²4 cm²14. If y = 3cos4x, find dy/dx-12sin4x12cos4x12sin4x-12cos4x15. 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 m16m12 m10 m16. Determine the turning point of the curve y = x² + 250/x(2, 7)(-5, 35)(-2, 7)(5, 35)17. Find the minimum value of the function3x²-x³210-118. Differentiate wrt x:x³(x - 1)3x+2x³ + 3x²(x-1)(x²+2)x1+x²19. Differentiate w.r.t x 5x³5x²15x5x15x²20. 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/s8π cm/s10π cm/s4π cm/s21. Differentiate w.r.t θ( sin θ / 3+ 2cos θ )3cos θ + 21/(3 + 2cos θ )²3cos θ + 2/(3 + 2cos θ )²3cos θ + 2/(3 + 2cos θ)22. 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.2s1s4s3s23. 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 = 43ms-²2ms-²6ms-²4ms-²24. Find the derivative of y = sin(2x³ + 3x - 4) wrt x(6x²+3)cos(2x³ + 3x - 4)cos(2x³ + 3x - 4)6xsin(2x³ + 3x - 4)sin4x+x25. Find the derivative of 3-x3x-13x²-13-x²26 out of 25
