Differentiate the following functions with respect to `(e^xlogx)/(x^2)`

Explanation

Let `y=frac{e^{x} log x}{x^{2}}`


On differentiating `y` with respect to `x`, we get



`frac{d y}{d x}=frac{d}{d x}(frac{e^{x} log x}{x^{2}})`



Recall that `(frac{u}{v})^{prime}=frac{v_{u^{prime}-u v^{prime}}}{v^{2}}` (quotient rule)



`Rightarrow frac{d y}{d x}=frac{(x^{2}) frac{d}{d x}(e^{x} log x)-(e^{x} log x) frac{d}{d x}(x^{2})}{(x^{2})^{2}}`


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