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Popular >

derivative of x/(1+x^3)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

limit as x approaches 0 of (1-4x)^{8/x}

x \to 0 lim ((1 - 4 x)^{\frac{8}{x}})

limit as x approaches 4 of 1/(2+sqrt(x))

x \to 4 lim (\frac{1}{2 + x})

derivative of y=sin^2(e^{sin^2(t)})derivative of

y = sin^{2} (e^{s i n^{2} (t)})

integral of cos(2x)e^{-x}

\int cos (2 x) e^{- x} d x

integral of (3x)/(sqrt(x+4))

\int \frac{3 x}{x + 4} d x

Frequently Asked Questions (FAQ)

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