What is the derivative of (x^{2/3}/(5+x+x^4)) ?

The derivative of (x^{2/3}/(5+x+x^4)) is (-10x^4-x+10)/(3x^{1/3)(5+x+x^4)^2}

What is the first derivative of (x^{2/3}/(5+x+x^4)) ?

The first derivative of (x^{2/3}/(5+x+x^4)) is (-10x^4-x+10)/(3x^{1/3)(5+x+x^4)^2}

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

\frac{- 10 x ^{4} - x + 10}{3 x ^{\frac{1}{3}} ( 5 + x + x ^{4} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 + x + x^{4}) = 4 x^{3} + 1

= \frac{\frac{2}{3 x ^{\frac{1}{3}}} ( 5 + x + x ^{4} ) - ( 4 x ^{3} + 1 ) x ^{\frac{2}{3}}}{( 5 + x + x ^{4} ) ^{2}}

Simplify

\frac{\frac{2}{3 x ^{\frac{1}{3}}} ( 5 + x + x ^{4} ) - ( 4 x ^{3} + 1 ) x ^{\frac{2}{3}}}{( 5 + x + x ^{4} ) ^{2}} : \frac{- 10 x ^{4} - x + 10}{3 x ^{\frac{1}{3}} ( 5 + x + x ^{4} ) ^{2}}

= \frac{- 10 x ^{4} - x + 10}{3 x ^{\frac{1}{3}} ( 5 + x + x ^{4} ) ^{2}}

\int 4 x + \frac{1}{4 x} d x

\int 5 x e^{- 2 x} d x

\frac{2}{s + 3}

\frac{s + 1}{( s ^{2} + 9 )}

f (x) = 2 x^{2} - 3 x - 2, at x = 6

What is the derivative of (x^{2/3}/(5+x+x^4)) ?
The derivative of (x^{2/3}/(5+x+x^4)) is (-10x^4-x+10)/(3x^{1/3)(5+x+x^4)^2}
What is the first derivative of (x^{2/3}/(5+x+x^4)) ?
The first derivative of (x^{2/3}/(5+x+x^4)) is (-10x^4-x+10)/(3x^{1/3)(5+x+x^4)^2}