What is the derivative of \sqrt[3]{5+9x^2} ?

The derivative of \sqrt[3]{5+9x^2} is (6x)/((5+9x^2)^{2/3)}

What is the first derivative of \sqrt[3]{5+9x^2} ?

The first derivative of \sqrt[3]{5+9x^2} is (6x)/((5+9x^2)^{2/3)}

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derivative of

\frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 9 x^{2})

= \frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 9 x^{2})

\frac{d}{d x} (5 + 9 x^{2}) = 18 x

= \frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \cdot 18 x

Simplify

\frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

= \frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

x \to 5 lim (ln (x - 5))

\frac{d}{d x} (e + L (x))

\frac{x ^{3}}{4}

y^{3} - x y^{2} = 4

y = \frac{3}{x + 7}

What is the derivative of \sqrt[3]{5+9x^2} ?
The derivative of \sqrt[3]{5+9x^2} is (6x)/((5+9x^2)^{2/3)}
What is the first derivative of \sqrt[3]{5+9x^2} ?
The first derivative of \sqrt[3]{5+9x^2} is (6x)/((5+9x^2)^{2/3)}