Differentiate the following function with respect to `x:` `10^(logsinx)`

Explanation

Let `y=10^{log sin x} ldots(i)`

Taking log both sides,

`log y=log 10^{log sin x}`

`Rightarrow log y=log sin x log 10`


`Rightarrow frac{1}{y} frac{d y}{d x}=log 10 frac{d}{d x} log sin x `

`Rightarrow frac{1}{y} frac{d y}{d x}=log 10 frac{1}{sin x} frac{d}{d x}(sin x) `

`Rightarrow frac{1}{y} frac{d y}{d x}=log 10left(frac{1}{sin x}right)(cos x) `

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