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 ) x - 1 \cdot ( 1 - x )}{x ^{2}}

Simplify

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

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

\frac{\partial}{\partial y} (\frac{x - y}{x + 2 y})

\frac{\partial}{\partial x} (y^{4} sin (4 x))

y^{^{''}} y^{^{'}} = 2

\int_{0}^{\infty} 10 e^{- 5 x} d x

x \to 1 lim (x^{2} + 2 x - 3)

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)