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

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

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

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

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

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

Solution steps

\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}}

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

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

Simplify

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

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

\int - \frac{1}{x ^{5}} d x

- \frac{x}{3 y}

\int \frac{2}{2 - e ^{x}} d x

\frac{d}{d x} (x^{y^{z}})

y = (3 x^{3} + 4)^{2}

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