What is the derivative of (4x/(1+x^3)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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