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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

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

Simplify

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

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

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

\int 18 d x

x \to 0 lim (\frac{x ^{5} + 4 x}{x})

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

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