How solve Derivatives of Trigonometric Functions?

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1 Answer
Jun 18, 2018

dfdx=3csc(6x)sin2(4x)[4cos(4x)cot(6x)sin(4x)]

Explanation:

First use the product rule:

dfdx=csc(6x)ddx(sin3(4x))+ddx(csc(6x))sin3(4x)

using now the chain rule:

dfdx=3csc(6x)sin2(4x)ddx(sin(4x))+ddx(csc(6x))sin3(4x)2csc(6x)

dfdx=12csc(6x)sin2(4x)cos(4x)6cot(6x)csc(6x)sin3(4x)2csc(6x)

and as the function is defined only for cscx0 we can simplify:

dfdx=12csc(6x)sin2(4x)cos(4x)3cot(6x)csc(6x)sin3(4x)

dfdx=3csc(6x)sin2(4x)[4cos(4x)cot(6x)sin(4x)]