What is the derivative of 1/(\sqrt[3]{(6x^2+5^2)}) ?

The derivative of 1/(\sqrt[3]{(6x^2+5^2)}) is -(8x)/((6x^2+5)^{5/3)}

What is the first derivative of 1/(\sqrt[3]{(6x^2+5^2)}) ?

The first derivative of 1/(\sqrt[3]{(6x^2+5^2)}) is -(8x)/((6x^2+5)^{5/3)}

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- \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

Solution steps

Apply exponent rule:

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

= \frac{d}{d x} (((6 x^{2} + 5)^{2})^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((6 x^{2} + 5)^{2})

= - \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((6 x^{2} + 5)^{2})

\frac{d}{d x} ((6 x^{2} + 5)^{2}) = 24 x (6 x^{2} + 5)

= - \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \cdot 24 x (6 x^{2} + 5)

Simplify

- \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \cdot 24 x (6 x^{2} + 5) : - \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

= - \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

\int \frac{k}{x ln ( x )} d x

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

\frac{d}{d x} (y z e^{x})

\frac{d y}{d x} = x y + 2 x + 3 y + 6

7 x^{2}, at x = 10

What is the derivative of 1/(\sqrt[3]{(6x^2+5^2)}) ?
The derivative of 1/(\sqrt[3]{(6x^2+5^2)}) is -(8x)/((6x^2+5)^{5/3)}
What is the first derivative of 1/(\sqrt[3]{(6x^2+5^2)}) ?
The first derivative of 1/(\sqrt[3]{(6x^2+5^2)}) is -(8x)/((6x^2+5)^{5/3)}