What is the derivative of (x^4/(5-x^3)) ?

The derivative of (x^4/(5-x^3)) is (20x^3-x^6)/((5-x^3)^2)

What is the first derivative of (x^4/(5-x^3)) ?

The first derivative of (x^4/(5-x^3)) is (20x^3-x^6)/((5-x^3)^2)

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\frac{d}{d x} (\frac{x ^{4}}{5 - x ^{3}})

\frac{20 x ^{3} - x ^{6}}{( 5 - x ^{3} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{5 - x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} ) ( 5 - x ^{3} ) - \frac{d}{d x} ( 5 - x ^{3} ) x ^{4}}{( 5 - x ^{3} ) ^{2}}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= \frac{4 x ^{3} ( 5 - x ^{3} ) - ( - 3 x ^{2} ) x ^{4}}{( 5 - x ^{3} ) ^{2}}

Simplify

\frac{4 x ^{3} ( 5 - x ^{3} ) - ( - 3 x ^{2} ) x ^{4}}{( 5 - x ^{3} ) ^{2}} : \frac{20 x ^{3} - x ^{6}}{( 5 - x ^{3} ) ^{2}}

= \frac{20 x ^{3} - x ^{6}}{( 5 - x ^{3} ) ^{2}}

l a pl a ce t r an s f or m 3 t e^{- t}

\int_{2}^{e + 1} \frac{1}{x - 1} d x

\frac{d y}{d x} + tan (x) y - sec (x) = 0

\frac{d}{d x} (26 - sec^{3} (4 x))

x \to \infty lim ((4^{x} + 8^{x})^{\frac{1}{2 \cdot x}})

What is the derivative of (x^4/(5-x^3)) ?
The derivative of (x^4/(5-x^3)) is (20x^3-x^6)/((5-x^3)^2)
What is the first derivative of (x^4/(5-x^3)) ?
The first derivative of (x^4/(5-x^3)) is (20x^3-x^6)/((5-x^3)^2)