What is the derivative of (-6x/(x^2+1)) ?

The derivative of (-6x/(x^2+1)) is -(6(-x^2+1))/((x^2+1)^2)

What is the first derivative of (-6x/(x^2+1)) ?

The first derivative of (-6x/(x^2+1)) is -(6(-x^2+1))/((x^2+1)^2)

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\frac{d}{d x} (\frac{- 6 x}{x ^{2} + 1})

- \frac{6 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 6 x}{x ^{2} + 1})

Simplify

\frac{- 6 x}{x ^{2} + 1} : - \frac{6 x}{x ^{2} + 1}

= \frac{d}{d x} (- \frac{6 x}{x ^{2} + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 6 \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}}

= - 6 \cdot \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

= - 6 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}}

Simplify

- 6 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}} : - \frac{6 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

= - \frac{6 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

9 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

\frac{d y}{d x} = x \cdot e^{- 2 x}

\int \frac{x - 1}{( x + 1 ) ( 2 x ^{2} + 3 )} d x

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

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

What is the derivative of (-6x/(x^2+1)) ?
The derivative of (-6x/(x^2+1)) is -(6(-x^2+1))/((x^2+1)^2)
What is the first derivative of (-6x/(x^2+1)) ?
The first derivative of (-6x/(x^2+1)) is -(6(-x^2+1))/((x^2+1)^2)