What is the derivative of 1/(\sqrt[3]{2x+1}) ?

The derivative of 1/(\sqrt[3]{2x+1}) is -2/(3(2x+1)^{4/3)}

What is the first derivative of 1/(\sqrt[3]{2x+1}) ?

The first derivative of 1/(\sqrt[3]{2x+1}) is -2/(3(2x+1)^{4/3)}

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- \frac{2}{3 ( 2 x + 1 ) ^{\frac{4}{3}}}

Solution steps

Apply exponent rule:

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

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

Apply the chain rule:

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

= - \frac{1}{3 ( 2 x + 1 ) ^{\frac{4}{3}}} \frac{d}{d x} (2 x + 1)

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

= - \frac{1}{3 ( 2 x + 1 ) ^{\frac{4}{3}}} \cdot 2

Simplify

- \frac{1}{3 ( 2 x + 1 ) ^{\frac{4}{3}}} \cdot 2 : - \frac{2}{3 ( 2 x + 1 ) ^{\frac{4}{3}}}

= - \frac{2}{3 ( 2 x + 1 ) ^{\frac{4}{3}}}

\frac{d}{d x} (cos (2 x - 1) \cdot tan (1 - 2 x))

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

\int tan (\frac{x}{2}) sec^{2} (\frac{x}{2}) d x

y^{^{'''}} + 4 y^{^{''}} = 3 x - 1

\int e^{(x + 3)} d x

What is the derivative of 1/(\sqrt[3]{2x+1}) ?
The derivative of 1/(\sqrt[3]{2x+1}) is -2/(3(2x+1)^{4/3)}
What is the first derivative of 1/(\sqrt[3]{2x+1}) ?
The first derivative of 1/(\sqrt[3]{2x+1}) is -2/(3(2x+1)^{4/3)}