Find the derivative of f(x) = x+1 x - Vidyadip

Question

Find the derivative of f(x) = $\frac{x+1}{x}$

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Answer

The given function is defined everywhere except at x = 0. We use the quotient rule with u = x + 1 and v = x. Hence u′ = 1 and v′ = 1.
Therefore, we have,
$\frac{d f(x)}{d x}=\frac{d}{d x}\left(\frac{x+1}{x}\right)=\frac{d}{d x}\left(\frac{u}{v}\right)$ $=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}=\frac{1(x)-(x+1) 1}{x^{2}}=-\frac{1}{x^{2}}$

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