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 w.r.t θ( sin θ / 3+ 2cos θ )3cos θ + 2/(3 + 2cos θ )²3cos θ + 23cos θ + 2/(3 + 2cos θ)1/(3 + 2cos θ )²2. A particle moves along a straight line from a fixed point O such that its distance s metres at time t seconds is given by s = 2 +8t - 0.5t². Find the velocity of the particle as it passes point O.4m/s8m/s16m/s10m/s3. If y = x² - 1/x, find dy/dx2 - x²2x + 1/x²3x1/2x²4. 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.252122295. Find the minimum value of the function3x²-x³-10216. Differentiate the function w.r.t x: y = 4(x² - 3)8x²6xx²-38x7. Differentiate w.r.t x 3x²+4x3x+46x+46x6x+4x8. Find the point (x, y) on the Euclidean plane where the curve y = 2x² -2x + 3 has 2 as gradient(1, 3)(5, 7)(3, 4)(2, 9)9. Differentiate the function wrt x:(2x-7)²28x²8x-28x+7xx²-1410. Find the derivative of f(x)=6x³ − 9x + 4x18x²-9x²+318-xx²-911. Find the minimum value of the function y = x³ + 3x² - 9x + 1-4-2-3-112. What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?4π cm³/s6π cm³/s8π cm³/s2π cm³/s13. Differentiate w.r.t x sin³x3sin²xcosx-3sin²xcosx-3cos²xsinx3sin²x14. Find the differential coefficient of y = -5/(x²+4) at the point (1, -1)2/5-2/5-5/25/215. Find the derivative of y = sin²(5x) wrt xsin5xcos5xxsin²5x10sin5xcos5xxcos²5x16. If y = 8x² - 5x, find the approximate change in y if x changes from 1 to 1.05.1.01.50.250.5517. Find the minimum value of the function 2x³ - 6x²-88-5518. Differentiate (x² - 1/x)² wrt x4x³ -2/x³ -22x²-22/x³ +3x +2x³-3x²+219. 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 cm²3cm²2cm²1cm²20. If x³ + y³+ 6xy = 0, find dy/dx by implicit differentiation(2y + x²)/ (2x + y²)- (2y + x²)/(2x + y²)- (2y + x²)/ yx/(2x + y²)21. Find the maximum and minimum values of thefunction 3x² - x³max = 1, min = -1max = 4, min = 0max = 10, min = 4max =-2, min = -622. Differentiate 5x - 1/x² from the first principle5 + 2/x²5 + 2/x2/ x35 + 2/x³23. An object dropped from rest has position s = 7t² metres below its starting point. At what time does the object have velocity of 35 m/s.14 s2.5 s2 s3 s24. Find the maximum value of the function 3x²-x³-24-31/225. Differentiate the functions wrt x:5(3x-4)²60x²60x+4x²30(3x-4)3x²+426 out of 25
