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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

n = 0 \sum \infty n e^{- \frac{n}{2}}

\int_{4}^{\infty} \frac{1}{x ^{2} - 1} d x

\frac{d}{d x} (e^{x} cosh (x))

x \to 0 - lim (\frac{x}{8 x ^{4} + 2 x})

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

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