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

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

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

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

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derivative of

\frac{1}{3 ( 1 + x ) ^{\frac{2}{3}}}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

t^{2}

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{- \frac{1}{2}})

1 + e^{0.5499 - 0.09 x}

y = cos (ln (4 x^{3}))

y = e^{x} sin (x) + cos (x) e^{x}

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