Use logarithmic differentiation to find the derivative of the function: y = (cos 2x) ^x.

Question

Mathematics

Francisco

18 February, 20:56

Use logarithmic differentiation to find the derivative of the function: y = (cos 2x) ^x.

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Salma Bruce · Answer 1

The derivative of the given function y = (cos 2x) ^x can be obtained by transforming the given expression into its logarithmic form.

y = (cos 2x) ^x

ln y = x ln (cos 2x)

dy/y = x * - dx/2 sin 2x + ln (cos 2x) dx

dy/dx = - xy/2 sin 2x + ln (cos 2x). This is the final answer