Differentiate the following with respect of `x : e^(xloga)+e^(alogx)+e^(aloga)`

Explanation

We have,

`frac{d}{d x}(e^{x log a}+e^{a log x}+e^{a log a}) `

`=frac{d}{d x}(e^{x log a})+frac{d}{d x}(e^{a log x})+frac{d}{d x}(e^{a log a}) `

`=e^{x log a} cdot log a+e^{a log x} cdot frac{a}{x}+0 `

`quad[because a cdot e^{x log a} text { is constant }] `

`=log a cdot e^{x log a}+frac{a}{x} e^{a log x} `

`=log a cdot a^{x}+frac{a}{x} x^{a} `

`quad[a^{x}` can be written as ` e^{x log a}] `

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