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Popular >

derivative of f(x)=(x-1)/(x^2)

Solution

derivative of

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

Solution

\frac{- x + 2}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x - 1 )}{( x ^{2} ) ^{2}} : \frac{- x + 2}{x ^{3}}

= \frac{- x + 2}{x ^{3}}

Popular Examples

(\partial)/(\partial x)(3x^2y+2xy^3)

\frac{\partial}{\partial x} (3 x^{2} y + 2 x y^{3})

sum from n=0 to infinity of e^{-1}

n = 0 \sum \infty e^{- 1}

integral from-1 to 1 of xe^x

\int_{- 1}^{1} x e^{x} d x

derivative of ln(x^2+3x)

\frac{d}{d x} (ln (x^{2} + 3 x))

derivative of 5(1-e^{-2x})

\frac{d}{d x} (5 (1 - e^{- 2 x}))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x-1)/(x^2) ?
The derivative of f(x)=(x-1)/(x^2) is (-x+2)/(x^3)
What is the first derivative of f(x)=(x-1)/(x^2) ?
The first derivative of f(x)=(x-1)/(x^2) is (-x+2)/(x^3)