What is the derivative of (x^2/(x^3+8)) ?

The derivative of (x^2/(x^3+8)) is (-x^4+16x)/((x^3+8)^2)

What is the first derivative of (x^2/(x^3+8)) ?

The first derivative of (x^2/(x^3+8)) is (-x^4+16x)/((x^3+8)^2)

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\frac{d}{d x} (\frac{x ^{2}}{x ^{3} + 8})

\frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{3} + 8})

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} + 8 ) - \frac{d}{d x} ( x ^{3} + 8 ) x ^{2}}{( x ^{3} + 8 ) ^{2}}

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

\frac{d}{d x} (x^{3} + 8) = 3 x^{2}

= \frac{2 x ( x ^{3} + 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} + 8 ) ^{2}}

Simplify

\frac{2 x ( x ^{3} + 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} + 8 ) ^{2}} : \frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

= \frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

What is the derivative of (x^2/(x^3+8)) ?
The derivative of (x^2/(x^3+8)) is (-x^4+16x)/((x^3+8)^2)
What is the first derivative of (x^2/(x^3+8)) ?
The first derivative of (x^2/(x^3+8)) is (-x^4+16x)/((x^3+8)^2)