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

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

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

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

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derivative of

\frac{x - 1}{x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

1 - 2 x y

\frac{d}{d t} (20 + 5 t)

3 x^{2} y

\frac{1}{a ^{x}}

e^{2} x + 1

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