What is the derivative of (2-5x/(3x^{1/3)}) ?

The derivative of (2-5x/(3x^{1/3)}) is (-10x-2)/(9x^{4/3)}

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

The first derivative of (2-5x/(3x^{1/3)}) is (-10x-2)/(9x^{4/3)}

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\frac{d}{d x} (\frac{2 - 5 x}{3 x ^{\frac{1}{3}}})

\frac{- 10 x - 2}{9 x ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} (\frac{2 - 5 x}{3 x ^{\frac{1}{3}}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 2 - 5 x ) x ^{\frac{1}{3}} - \frac{d}{d x} ( x ^{\frac{1}{3}} ) ( 2 - 5 x )}{( x ^{\frac{1}{3}} ) ^{2}}

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

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

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

Simplify

\frac{1}{3} \cdot \frac{( - 5 ) x ^{\frac{1}{3}} - \frac{1}{3 x ^{\frac{2}{3}}} ( 2 - 5 x )}{( x ^{\frac{1}{3}} ) ^{2}} : \frac{- 10 x - 2}{9 x ^{\frac{4}{3}}}

= \frac{- 10 x - 2}{9 x ^{\frac{4}{3}}}

x \to \infty lim (\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2})

\int 1 4^{x} d x

f (x) = 4 + 3 ln (x), at x = 1

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

\int \frac{x ^{3} + x + 1}{x ^{2} - 4 x + 3} d x

What is the derivative of (2-5x/(3x^{1/3)}) ?
The derivative of (2-5x/(3x^{1/3)}) is (-10x-2)/(9x^{4/3)}
What is the first derivative of (2-5x/(3x^{1/3)}) ?
The first derivative of (2-5x/(3x^{1/3)}) is (-10x-2)/(9x^{4/3)}