What is the derivative of $y=(lnx)^(cosx)$ ?

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Answer 1 · 2017-03-07T06:18:56

Use substitution

$ln y = cos x ln(ln(x))$
$1/y dy/dx = sin x ln(ln x)+cosx 1/ln(x) 1/x$
$dy/dx = (ln x)^(cos x)\times (sin x ln(ln x)+cosx 1/ln(x) 1/x)$

What is the derivative of y=(lnx)^(cosx)y=(lnx)^(cosx)?