What is the derivative of 2/(\sqrt[5]{(4x-1^3)}) ?

The derivative of 2/(\sqrt[5]{(4x-1^3)}) is -(24)/(5(4x-1)^{8/5)}

What is the first derivative of 2/(\sqrt[5]{(4x-1^3)}) ?

The first derivative of 2/(\sqrt[5]{(4x-1^3)}) is -(24)/(5(4x-1)^{8/5)}

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- \frac{24}{5 ( 4 x - 1 ) ^{\frac{8}{5}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

= 2 \frac{d}{d x} (((4 x - 1)^{3})^{- \frac{1}{5}})

Apply the chain rule:

- \frac{1}{5 ( ( 4 x - 1 ) ^{3} ) ^{\frac{6}{5}}} \frac{d}{d x} ((4 x - 1)^{3})

= - \frac{1}{5 ( ( 4 x - 1 ) ^{3} ) ^{\frac{6}{5}}} \frac{d}{d x} ((4 x - 1)^{3})

\frac{d}{d x} ((4 x - 1)^{3}) = 12 (4 x - 1)^{2}

= 2 - \frac{1}{5 ( ( 4 x - 1 ) ^{3} ) ^{\frac{6}{5}}} \cdot 12 (4 x - 1)^{2}

Simplify

2 - \frac{1}{5 ( ( 4 x - 1 ) ^{3} ) ^{\frac{6}{5}}} \cdot 12 (4 x - 1)^{2} : - \frac{24}{5 ( 4 x - 1 ) ^{\frac{8}{5}}}

= - \frac{24}{5 ( 4 x - 1 ) ^{\frac{8}{5}}}

\frac{d}{d x} (\frac{8 x ^{2} + 2 x + 2}{x})

(80, 2000), (260, 5600)

x \to 1 lim (e^{x})

\int_{2}^{7} \frac{1}{25 + ( x - 2 ) ^{2}} d x

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

What is the derivative of 2/(\sqrt[5]{(4x-1^3)}) ?
The derivative of 2/(\sqrt[5]{(4x-1^3)}) is -(24)/(5(4x-1)^{8/5)}
What is the first derivative of 2/(\sqrt[5]{(4x-1^3)}) ?
The first derivative of 2/(\sqrt[5]{(4x-1^3)}) is -(24)/(5(4x-1)^{8/5)}