Differentiation Exercises

Find the derivatives of the following functions from the first principles. a) y = 3x^5 b) y = 3/(2x) c) y = x^4 -

Differentiate each of the following with respect to x. a) 3/(2x)e b) x e^3 c) e^(2 tan x) d) e^(cot x)

Differentiate each of the following with respect to x. a) ln (cos^2(2x)) b) ln(x^3(3x - 1)^4) c) x^25ln - d) (13/12)ln(x/x)

Differentiate each of the following with respect to x. a) sin(x^2) b) cos(3x - 2) c) 2 tan^2(3x + 2) d) sec^3(2 - 3x)

Find dy/dx for each of the following functions. a) y = x^3 ln(x^2 + 4) b) y = e^(-2x)(2 cos(3x) - 3 sin(3x)) c) y = (x/e^x)sin^2 d) y = (x/e^x)cos e) y = (x/e^x)^2 sin f) y = (x/x)e^x sin

Find dy/dx in terms of x and y for each of the following implicit functions, a) x^3 - 2xy - y^3 = 4 b) 3(x - y)^2 = 2xy + 6 c) x^2 + y^2 - 2xy + 3y - 2x = 5 d) 2xe^y + 3ye^x = 1 e) x ln y + y ln x = 7 f) x sin(2y) - y cos(3x) = 5

Find dy/dx for each of the following functions. a) y = 6/x b) y = 3/(9x) c) y = 7 cos x

Differentiate each of the following functions with respect to x. a) cos^(-1)(x) b) (1 - x^2)^(1/2) c) tan^(-1)(2x)

Given that y(1 + x) = x, show that (0) = (2) + (1) + (2).

Given that y = (1 + 4x)e^(-2x), show that (0) = (2) + (1) + (2).