What is the derivative of 1/(\sqrt[3]{4x^2-7}) ?

The derivative of 1/(\sqrt[3]{4x^2-7}) is -(8x)/(3(4x^2-7)^{4/3)}

What is the first derivative of 1/(\sqrt[3]{4x^2-7}) ?

The first derivative of 1/(\sqrt[3]{4x^2-7}) is -(8x)/(3(4x^2-7)^{4/3)}

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- \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

Solution steps

Apply exponent rule:

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

= \frac{d}{d x} ((4 x^{2} - 7)^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \frac{d}{d x} (4 x^{2} - 7)

= - \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \frac{d}{d x} (4 x^{2} - 7)

\frac{d}{d x} (4 x^{2} - 7) = 8 x

= - \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \cdot 8 x

Simplify

- \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \cdot 8 x : - \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

= - \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

\frac{\partial}{\partial y} (- \frac{x}{y ^{2}})

x y d x + (x^{2} + y^{2}) d y = 0

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What is the derivative of 1/(\sqrt[3]{4x^2-7}) ?
The derivative of 1/(\sqrt[3]{4x^2-7}) is -(8x)/(3(4x^2-7)^{4/3)}
What is the first derivative of 1/(\sqrt[3]{4x^2-7}) ?
The first derivative of 1/(\sqrt[3]{4x^2-7}) is -(8x)/(3(4x^2-7)^{4/3)}