Find derivative of the given function $(cos x)^{x}$ .

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Solution

$y = (cos x)^{x}$

By Taking log on Both Side

$log y = x log cos x$

$\frac{1}{y} \frac{d y}{d x} = log cos x - x tan x$

$\frac{d y}{d x} = (cos x)^{x} [log cos x - x tan x]$

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Find derivative of the given function (cosx)x.

y=(cosx)xBy Taking log on Both Sidelogy=xlogcosx1ydydx=logcosx−xtanxdydx=(cosx)x[logcosx−xtanx]

Find derivative of the given function $(cos x)^{x}$ .

$y = (cos x)^{x}$

By Taking log on Both Side

$log y = x log cos x$

$\frac{1}{y} \frac{d y}{d x} = log cos x - x tan x$

$\frac{d y}{d x} = (cos x)^{x} [log cos x - x tan x]$