Find the derivative of the function, f(x) = ln[sin^2(3x)] Find the derivative of

Question

Find the derivative of the function, f(x) = ln[sin^2(3x)] Find the derivative of the function. f(theta) = theta^2 Tan (theta) Find dy/dx for the equation, y = (e^3x + x^2)^3 Find dy/dx for the equation, y = (e^3x + x^2)^3 Find the dy/dx for the following equation implicitly (y^2 + 2)^3 = x^4 y + 11 The blade of a saber saw moves up and down, and its displacement y (in cm) is given by y = 1.85 Cos (36 pi t), where t is the time (in seconds). Find the velocity of the blade for t = 0.025 seconds and the acceleration of the blade for t = 0.025 seconds. The voltage V induced in an inductor in an electric circuit is given by V = L(d^2q/dt^2), where L is the inductance (in Henry). Find the expression tor the voltage induced in a 1.60 H inductor if q = 0.5(1 - e^-10t) Find the expression for voltage induced in a 1.60H inductor if q = 0.5(1 - e^-10t) The strength, S, of a beam with a rectangular cross section is directly proportional to the product of its width, w, and the square of its depth, d. Find the dimension of the strongest beam that can be cut from a log with a circular cross section that is 16 inches in diameter.

Explanation / Answer

(1) f(x) = ln(sin^3 3x)

f'(x) = [1/(sin^3 3x)] (3 sin^2 3x)(cos 3x)(3) = (9 cos 3x)/sin 3x = 9 cot 3x

(2) f() = ()^2 tan

f'() = ()^2 sec^2 + (tan )(2 ) = ()^2 sec^2 + 2 tan

(3) y = (e^3x + x^2)^3

dy/dx = 3[e^(3x) + x^2)]^2 * [3e^(3x) + 2x)]

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