What is the derivative of (-4x/(x^2+1)) ?

The derivative of (-4x/(x^2+1)) is -(4(-x^2+1))/((x^2+1)^2)

What is the first derivative of (-4x/(x^2+1)) ?

The first derivative of (-4x/(x^2+1)) is -(4(-x^2+1))/((x^2+1)^2)

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\frac{d}{d x} (\frac{- 4 x}{x ^{2} + 1})

- \frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 4 x}{x ^{2} + 1})

Simplify

\frac{- 4 x}{x ^{2} + 1} : - \frac{4 x}{x ^{2} + 1}

= \frac{d}{d x} (- \frac{4 x}{x ^{2} + 1})

Take the constant out:

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

= - 4 \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}}

= - 4 \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

= - 4 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}}

Simplify

- 4 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}} : - \frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

= - \frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

f (x) = \frac{x ^{3} - 3 x ^{2} + 4}{x ^{2}}

5 - x^{2}, sin (x), - 2.38468, 2.02521

7 e^{3 t} - 8 e^{- t} + 3

\int tan^{- 3} (x) sec^{4} (x) d x

\int_{- 10}^{x} t^{2} + 11 d t

What is the derivative of (-4x/(x^2+1)) ?
The derivative of (-4x/(x^2+1)) is -(4(-x^2+1))/((x^2+1)^2)
What is the first derivative of (-4x/(x^2+1)) ?
The first derivative of (-4x/(x^2+1)) is -(4(-x^2+1))/((x^2+1)^2)