What is the derivative of-2/(9(1+x)^{5/3)} ?

The derivative of-2/(9(1+x)^{5/3)} is (10)/(27(1+x)^{8/3)}

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

The first derivative of-2/(9(1+x)^{5/3)} is (10)/(27(1+x)^{8/3)}

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derivative

\frac{10}{27 ( 1 + x ) ^{\frac{8}{3}}}

Solution steps

\frac{d}{d x} (- \frac{2}{9 ( 1 + x ) ^{\frac{5}{3}}})

Take the constant out:

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

= - \frac{2}{9} \frac{d}{d x} (\frac{1}{( 1 + x ) ^{\frac{5}{3}}})

Apply exponent rule:

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

= - \frac{2}{9} \frac{d}{d x} ((1 + x)^{- \frac{5}{3}})

Apply the chain rule:

- \frac{5}{3 ( 1 + x ) ^{\frac{8}{3}}} \frac{d}{d x} (1 + x)

= - \frac{5}{3 ( 1 + x ) ^{\frac{8}{3}}} \frac{d}{d x} (1 + x)

\frac{d}{d x} (1 + x) = 1

= - \frac{2}{9} (- \frac{5}{3 ( 1 + x ) ^{\frac{8}{3}}} \cdot 1)

Simplify

- \frac{2}{9} (- \frac{5}{3 ( 1 + x ) ^{\frac{8}{3}}} \cdot 1) : \frac{10}{27 ( 1 + x ) ^{\frac{8}{3}}}

= \frac{10}{27 ( 1 + x ) ^{\frac{8}{3}}}

What is the derivative of-2/(9(1+x)^{5/3)} ?
The derivative of-2/(9(1+x)^{5/3)} is (10)/(27(1+x)^{8/3)}
What is the first derivative of-2/(9(1+x)^{5/3)} ?
The first derivative of-2/(9(1+x)^{5/3)} is (10)/(27(1+x)^{8/3)}