Find the derivative of y = cos(x)^(sin(x))
In normal derivation we know that;
`(d(x^n))/dx = nx^(n-1)`
This is valid only when n is a constant or n is not a function of x.
For our question we cannot use the above rule because sinx is not a constant.
So we have to use logarithm method to solve this.
`y = cos(x)^(sin(x))`
Take log in both sides.
`logy = log(cos(x)^(sin(x)))`
`logy = sinxlogcosx`
Get the derivative on both sides.
`1/y*(dy)/dx = sinx*1/cosx*(-sinx)+logcosx*cosx`
` (dy)/dx = y(cosxlogcosx-(sin^2x)/cosx)`
`(dy)/dx = (cos(x)^(sin(x)))(cosxlogcosx-(sin^2x)/cosx)`
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