What is the derivative of f(x)=(x-5)/x ?

The derivative of f(x)=(x-5)/x is 5/(x^2)

What is the first derivative of f(x)=(x-5)/x ?

The first derivative of f(x)=(x-5)/x is 5/(x^2)

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derivative of

f (x) = \frac{x - 5}{x}

\frac{5}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) x - \frac{d x}{d x} ( x - 5 )}{x ^{2}}

\frac{d}{d x} (x - 5) = 1

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

= \frac{1 \cdot x - 1 \cdot ( x - 5 )}{x ^{2}}

Simplify

\frac{1 \cdot x - 1 \cdot ( x - 5 )}{x ^{2}} : \frac{5}{x ^{2}}

= \frac{5}{x ^{2}}

\int x \cdot arcsin (x^{2}) d x

\int t^{9} e^{- t^{10}} d t

\int_{1}^{4} (2 - x^{2}) - (6 - 5 x) d x

\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

(x^{2} - 24)^{6}

What is the derivative of f(x)=(x-5)/x ?
The derivative of f(x)=(x-5)/x is 5/(x^2)
What is the first derivative of f(x)=(x-5)/x ?
The first derivative of f(x)=(x-5)/x is 5/(x^2)