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

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

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

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

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derivative of

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

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

- 5 sin (5 t)

\frac{d ^{2}}{d x ^{2}} (x^{- \frac{1}{11}})

\int u (x) d x

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