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Popular >

derivative of (x^2/(x^3+1))

Solution

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

Solution

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

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) = 3 x^{2}

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

Simplify

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

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

Graph

Popular Examples

derivative of 1/(x^{10)}derivative of

\frac{1}{x ^{10}}

derivative of 4/(x^7-e^{-8x})

\frac{d}{d x} (\frac{4}{x ^{7}} - e^{- 8 x})

integral of x/((x+1)(x+2))

\int \frac{x}{( x + 1 ) ( x + 2 )} d x

(\partial)/(\partial x)(1.015sqrt(E(m,x)bh^3m^{-1)L^{-4}})

\frac{\partial}{\partial x} (1.015 E (m, x) b h^{3} m^{- 1} L^{- 4})

derivative of cot^4(x-csc^4(x))

\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

Frequently Asked Questions (FAQ)

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