What is the derivative of (1+x/x) ?

The derivative of (1+x/x) is -1/(x^2)

What is the first derivative of (1+x/x) ?

The first derivative of (1+x/x) is -1/(x^2)

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\frac{d}{d x} (\frac{1 + x}{x})

- \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 + x}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 1 + x ) x - \frac{d x}{d x} ( 1 + x )}{x ^{2}}

\frac{d}{d x} (1 + x) = 1

\frac{d x}{d x} = 1

= \frac{1 \cdot x - 1 \cdot ( 1 + x )}{x ^{2}}

Simplify

\frac{1 \cdot x - 1 \cdot ( 1 + x )}{x ^{2}} : - \frac{1}{x ^{2}}

= - \frac{1}{x ^{2}}

\frac{d}{d x} ((a - \frac{b}{x})^{2})

\frac{2.4}{5 + 1 x}

\int \frac{x}{4 - x} d x

y = ln (ln (8 x))

e^{(e^{x})}

What is the derivative of (1+x/x) ?
The derivative of (1+x/x) is -1/(x^2)
What is the first derivative of (1+x/x) ?
The first derivative of (1+x/x) is -1/(x^2)