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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim (4 x^{2} - 2 x + 3)

\int \frac{x}{1 0 ^{x}} d x

a re a 10 - 7 x, x^{2} - 20, 0

\frac{d}{d x} (x^{6} f (x))

f (u) = ln (u)

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