What is the derivative of (3x^2/(1+x^3)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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