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(-x^3+5)^4)/(((5-x^3)^5)^{4/3)}

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(-x^3+5)^4)/(((5-x^3)^5)^{4/3)}

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derivative of

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

\frac{5 x ^{2} ( - x ^{3} + 5 ) ^{4}}{( ( 5 - x ^{3} ) ^{5} ) ^{\frac{4}{3}}}

Solution steps

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

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

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

y^{^{'}} + 4 x y = x^{3} e^{x^{2}}, y (0) = - 1

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

\frac{e ^{- s}}{( s + 1 ) ^{2} + 1}

\int_{0}^{π} 2 sin^{4} (x) d x

\int \frac{x ^{3}}{x ^{2} + x + 1} 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(-x^3+5)^4)/(((5-x^3)^5)^{4/3)}
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(-x^3+5)^4)/(((5-x^3)^5)^{4/3)}