What is the derivative of 5/(\sqrt[3]{x}) ?

The derivative of 5/(\sqrt[3]{x}) is -5/(3x^{4/3)}

What is the first derivative of 5/(\sqrt[3]{x}) ?

The first derivative of 5/(\sqrt[3]{x}) is -5/(3x^{4/3)}

\frac{d}{d x} (\frac{5}{3 x})

- \frac{5}{3 x ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} (\frac{5}{3 x})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{5}{3 x ^{\frac{4}{3}}}

x^{3} y^{^{'}} = e^{y}

\int 5 y d y

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

\int sec (x) tan (x) sin (sec (x)) d x

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

What is the derivative of 5/(\sqrt[3]{x}) ?
The derivative of 5/(\sqrt[3]{x}) is -5/(3x^{4/3)}
What is the first derivative of 5/(\sqrt[3]{x}) ?
The first derivative of 5/(\sqrt[3]{x}) is -5/(3x^{4/3)}