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

The derivative of (sqrt(x))/(x^3+1) is (-5x^3+1)/(2sqrt(x)(x^3+1)^2)

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

The first derivative of (sqrt(x))/(x^3+1) is (-5x^3+1)/(2sqrt(x)(x^3+1)^2)

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derivative of

\frac{x}{x ^{3} + 1}

\frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

\frac{\frac{1}{2 x} ( x ^{3} + 1 ) - 3 x ^{2} x}{( x ^{3} + 1 ) ^{2}} : \frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

= \frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

What is the derivative of (sqrt(x))/(x^3+1) ?
The derivative of (sqrt(x))/(x^3+1) is (-5x^3+1)/(2sqrt(x)(x^3+1)^2)
What is the first derivative of (sqrt(x))/(x^3+1) ?
The first derivative of (sqrt(x))/(x^3+1) is (-5x^3+1)/(2sqrt(x)(x^3+1)^2)