(1) Find the derivative of y = x cos x Solution
(2) Find the derivative of y = x log x + (log x)x Solution
(3) Find the derivative of √(xy) = e x - y Solution
(4) Find the derivatives of the following
xy = yx Solution
(5) Find the derivatives of the following
y = (cos x) log x Solution
(6) Find the derivatives of the following
(x2/a2) + (y2/b2) = 1 Solution
(7) Find the derivatives of the following
√(x2 + y2) = tan-1(y/x) Solution
(8) Differentiate the following
tan (x + y) + tan (x - y) = x Solution
(9) Differentiate the following
If cos (xy) = x, show that dy/dx = -(1+ysin(xy))/x sin(xy)
(10) Differentiate the following
tan-1[√(1 - cos x)/(1+cosx)] Solution
(11) Differentiate the following
tan-1[6x/1-9x2] Solution
(12) Differentiate the following
cos (2tan-1[√(1-x)/(1+x)]) Solution
(13) Differentiate the following
x = a cos3t, y = a sin3t Solution
(14) Differentiate the following
x = a (cos t + t sin t) ; y = a (sin t - t cos t) Solution
(15) Differentiate the following
x = (1-t2)/(1+t2) ; y = 2t/(1+t2) Solution
(16) Differentiate the following
cos-1(1 -x2)/(1+x2) Solution
(17) Differentiate the following
sin-1(3x - 4x3) Solution
(18) Differentiate the following
tan-1[(cos x + sin x) / (cos x - sin x)] Solution
(19) Find the derivative of sin x2 with respect to x2
(20) Find the derivative of sin-1(2x / (1 + x2)) with respect to tan-1 x Solution
(21) Differentiate the following
If u = tan-1 [√(1+x2) - 1]/x and v = tan-1x, find du/dv Solution
(22) Find the derivative with tan-1 (sin x/(1 + cos x)) with respect to tan-1 (cos x/(1 + sin x)) Solution
(23) If y = sin-1x then find y'' Solution
(24) If y = e^(tan-1x) show that (1+ x2 ) y'' + (2x −1) y' = 0. Solution
(25) If y = sin-1 x/√(1-x2) show that (1-x2)y2 - 3xy1 - y = 0 Solution
(26) If x = a (θ + sin θ), y = a (1 - cos θ) then prove that at θ = π/2, y'' = 1/a Solution
(27) If sin y = x sin(a + y), then prove that dy/dx = sin2 (a + y)/sin a , a ≠ nπ Solution
(28) If y = (cos-1x)2 prove that (1 -x2)(d2y/dx2) - x (dy/dx) - 2 = 0 Solution
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