Differentiate the following with respect of `x :(2x^2+3x+4)/x`

Explanation

Glven,

`f(x)=frac{2 x^{2}+3 x+4}{x} `

`Rightarrow f(x)=2 x+3+frac{4}{x} `

`Rightarrow f(x)=2 x+3+4 x-1`

`therefore frac{d}{d x}{f(x)}=frac{d}{d x}(2 x+3+4 x^{-1})`

algebra of derivatives -

`Rightarrow f^{prime}(x)=2 frac{d}{d x}(x)+frac{d}{d x}(3)+4 frac{d}{d x}(x^{-1})`

formula: `frac{d}{d x}(x^{n})=n x^{n-1}`

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