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

The derivative of (2x/(x^4+1)) is (2(-3x^4+1))/((x^4+1)^2)

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

The first derivative of (2x/(x^4+1)) is (2(-3x^4+1))/((x^4+1)^2)

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

\frac{2 ( - 3 x ^{4} + 1 )}{( x ^{4} + 1 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{4} + 1) = 4 x^{3}

= 2 \cdot \frac{1 \cdot ( x ^{4} + 1 ) - 4 x ^{3} x}{( x ^{4} + 1 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{4} + 1 ) - 4 x ^{3} x}{( x ^{4} + 1 ) ^{2}} : \frac{2 ( - 3 x ^{4} + 1 )}{( x ^{4} + 1 ) ^{2}}

= \frac{2 ( - 3 x ^{4} + 1 )}{( x ^{4} + 1 ) ^{2}}

\int_{1}^{4} - 10 t ln (t) d t

\int 10 x^{5} e^{- x^{3}} d x

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

A x + B

e^{-, at}

What is the derivative of (2x/(x^4+1)) ?
The derivative of (2x/(x^4+1)) is (2(-3x^4+1))/((x^4+1)^2)
What is the first derivative of (2x/(x^4+1)) ?
The first derivative of (2x/(x^4+1)) is (2(-3x^4+1))/((x^4+1)^2)