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

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

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

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

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derivative of

\frac{x - y}{x}

\frac{y}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{2} ( x + 3 )}{16 ( x ^{2} - 4 )})

\frac{d y}{d x} = y, y (11) = 3

\int \frac{1}{x ^{2} - x - 6} d x

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

f (x) = \frac{( x )}{x - 4}

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