What is the derivative of (40/(3x^{1/3)}) ?

The derivative of (40/(3x^{1/3)}) is -(40)/(9x^{4/3)}

What is the first derivative of (40/(3x^{1/3)}) ?

The first derivative of (40/(3x^{1/3)}) is -(40)/(9x^{4/3)}

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\frac{d}{d x} (\frac{40}{3 x ^{\frac{1}{3}}})

- \frac{40}{9 x ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} (\frac{40}{3 x ^{\frac{1}{3}}})

Take the constant out:

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

= \frac{40}{3} \frac{d}{d x} (\frac{1}{x ^{\frac{1}{3}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{40}{3} \frac{d}{d x} (x^{- \frac{1}{3}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{40}{3} (- \frac{1}{3} x^{- \frac{1}{3} - 1})

Simplify

\frac{40}{3} (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{40}{9 x ^{\frac{4}{3}}}

= - \frac{40}{9 x ^{\frac{4}{3}}}

x \to 0 lim (\frac{x + 4 - 2}{sin ( 5 x )})

\int 39 arctan (x) d x

\int 6 t sin (t) d t

y = 5 x - x^{2}, x

x \to 0 lim (\frac{1}{x ^{2} - x})

What is the derivative of (40/(3x^{1/3)}) ?
The derivative of (40/(3x^{1/3)}) is -(40)/(9x^{4/3)}
What is the first derivative of (40/(3x^{1/3)}) ?
The first derivative of (40/(3x^{1/3)}) is -(40)/(9x^{4/3)}