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derivative of f(x)=(1-x)/x

Solution

derivative of

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

Solution

- \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}}

Popular Examples

derivative of xsin(xcos(x))

\frac{d}{d x} (x sin (x) cos (x))

integral of x^{10}

\int x^{10} d x

integral from 0 to 2 of e^{-3x}

\int_{0}^{2} e^{- 3 x} d x

y^{''}+y^'-6y=6t-7-(20te^{2t}+14e^{2t})

y^{^{''}} + y^{^{'}} - 6 y = 6 t - 7 - (20 t e^{2 t} + 14 e^{2 t})

tangent of f(x)=x^6,\at x=2 tangent of

f (x) = x^{6}, at x = 2

Frequently Asked Questions (FAQ)

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