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DerivativE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

+1 vote

If h(x) = tan(3x) / x^2 , find the derivative of h(x).

asked Feb 26, 2013 in CALCULUS by johnkelly Apprentice

1 Answer

0 votes

The function h (x) = tan(3x) / x2 .

h (x) = tan(3x) * x- 2 .

Differentiate the function with respect to x.

h ' (x) = [ tan(3x) * x- 2 ] '.

Apply product rule : (uv) ' = uv ' + vu ' .

h ' (x) = tan(3x) * (x- 2) ' + x- 2(tan 3x) '

Apply formulas : (xn) ' = nxn - 1

                          (tan x) ' = sec2 x.

h ' (x) = - 2tan(3x)(x- 3) + 3x- 2(sec2 3x)

h ' (x) = [ - 2tan(3x)/(x3) ] + [ 3(sec2 3x)/x2 ]

h ' (x) = [ 3x(sec2 3x) - 2tan(3x)] / x3 .

The derivative of h(x) is [ 3x(sec2 3x) - 2tan(3x)] / x3 .

answered Jul 30, 2014 by lilly Expert

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