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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

(\partial)/(\partial z)(x*sin(y)*sin(z))

\frac{\partial}{\partial z} (x \cdot sin (y) \cdot sin (z))

(\partial)/(\partial y)(y/x+6x)

\frac{\partial}{\partial y} (\frac{y}{x} + 6 x)

slope of 3^{x^2-1},\at x=2

s l o p e 3^{x^{2} - 1}, at x = 2

integral of 1/3

\int \frac{1}{3} d x

integral of 4x^{-2}+3x^{-1}-1

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

Frequently Asked Questions (FAQ)

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