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

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

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

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

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\frac{5 x ^{2}}{( 5 - x ^{3} ) ^{\frac{8}{3}}}

Solution steps

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((5 - x^{3})^{5}) = - 15 x^{2} (5 - x^{3})^{4}

= - \frac{1}{3 ( ( 5 - x ^{3} ) ^{5} ) ^{\frac{4}{3}}} (- 15 x^{2} (5 - x^{3})^{4})

Simplify

- \frac{1}{3 ( ( 5 - x ^{3} ) ^{5} ) ^{\frac{4}{3}}} (- 15 x^{2} (5 - x^{3})^{4}) : \frac{5 x ^{2}}{( 5 - x ^{3} ) ^{\frac{8}{3}}}

= \frac{5 x ^{2}}{( 5 - x ^{3} ) ^{\frac{8}{3}}}

n = 0 \sum \infty \frac{( 2 ^{n + 1} )}{5 ^{n}}

\int \frac{x}{5 x + 3} d x

\int \frac{1}{100} x + 10 d x

\frac{\partial}{\partial x} (ln (x^{7} + y^{3}))

\int_{0}^{8} 1 + 9 x d x

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