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

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

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

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

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

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

Solution steps

\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}}

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

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

Simplify

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

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

\frac{\partial}{\partial x} (e^{- y} + e^{- x})

f (x) = 4 sin (4 x)

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

x^{^{'}} + 6 x = 0

n = 0 \sum \infty 3 \cdot (- \frac{2}{5})^{n}

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