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

Textbook Question

Chapter 3, 3.6 - Problem 44 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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`y = x^(cosx)`

taking log to the base 'e' both sides we get

`lny = (cosx)*lnx`

Thus, `(1/y)*dy/dx = -sinx*(lnx) + (cosx/x)`

`or, dy/dx = y*[(cosx/x) - sinx*(lnx)]`

`or, dy/dx = x^(cosx)*[(cosx/x) - sinx*(logx)]`

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