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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of 1/(e^x-4e^{-x)}

\int \frac{1}{e ^{x} - 4 e ^{- x}} d x

y^'=((y^4-1))/(4xy^3)

y^{^{'}} = \frac{( y ^{4} - 1 )}{4 x y ^{3}}

integral of 8/(w^2sqrt(4-w^2))

\int \frac{8}{w ^{2} 4 - w ^{2}} d w

derivative of x^4-3

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

(dy)/(dx)=e^{-a*x}-b*y,y(0)=0

\frac{d y}{d x} = e^{- a \cdot x} - b \cdot y, y (0) = 0

Frequently Asked Questions (FAQ)

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