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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(x^{0.5}y^{0.5}z)

\frac{\partial}{\partial x} (x^{0.5} y^{0.5} z)

(x+2)^2y^'+8y=5-4xy

(x + 2)^{2} y^{^{'}} + 8 y = 5 - 4 x y

limit as x approaches 4 of x^2-5x+7x^3

x \to 4 lim (x^{2} - 5 x + 7 x^{3})

derivative of 1/(2e^2e^{2x})

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

integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2

\int \frac{( u ^{2} ) ^{22}}{1 + ( u ^{2} ) ^{22}} d (u^{2})^{2}

Frequently Asked Questions (FAQ)

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