What is the derivative of 5/(\sqrt[3]{x^8}) ?

The derivative of 5/(\sqrt[3]{x^8}) is -(40)/(3x^{11/3)}

What is the first derivative of 5/(\sqrt[3]{x^8}) ?

The first derivative of 5/(\sqrt[3]{x^8}) is -(40)/(3x^{11/3)}

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- \frac{40}{3 x ^{\frac{11}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{8})

= - \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= 5 (- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \cdot 8 x^{7})

Simplify

5 (- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \cdot 8 x^{7}) : - \frac{40}{3 x ^{\frac{11}{3}}}

= - \frac{40}{3 x ^{\frac{11}{3}}}

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

x e^{x}, 1 \leq x \leq 7

\frac{\partial}{\partial x} (x^{2} y^{\frac{1}{3}})

\frac{d}{d t} (e^{- t} - e^{- t} t)

f (x) = e^{x c o s (x)}

What is the derivative of 5/(\sqrt[3]{x^8}) ?
The derivative of 5/(\sqrt[3]{x^8}) is -(40)/(3x^{11/3)}
What is the first derivative of 5/(\sqrt[3]{x^8}) ?
The first derivative of 5/(\sqrt[3]{x^8}) is -(40)/(3x^{11/3)}