What is the derivative of f(x)=\sqrt[3]{36x^2+10} ?

The derivative of f(x)=\sqrt[3]{36x^2+10} is (24x)/((36x^2+10)^{2/3)}

What is the first derivative of f(x)=\sqrt[3]{36x^2+10} ?

The first derivative of f(x)=\sqrt[3]{36x^2+10} is (24x)/((36x^2+10)^{2/3)}

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derivative of

f (x) = 3 36 x^{2} + 10

\frac{24 x}{( 36 x ^{2} + 10 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 36 x^{2} + 10)

Apply the chain rule:

\frac{1}{3 ( 36 x ^{2} + 10 ) ^{\frac{2}{3}}} \frac{d}{d x} (36 x^{2} + 10)

= \frac{1}{3 ( 36 x ^{2} + 10 ) ^{\frac{2}{3}}} \frac{d}{d x} (36 x^{2} + 10)

\frac{d}{d x} (36 x^{2} + 10) = 72 x

= \frac{1}{3 ( 36 x ^{2} + 10 ) ^{\frac{2}{3}}} \cdot 72 x

Simplify

\frac{1}{3 ( 36 x ^{2} + 10 ) ^{\frac{2}{3}}} \cdot 72 x : \frac{24 x}{( 36 x ^{2} + 10 ) ^{\frac{2}{3}}}

= \frac{24 x}{( 36 x ^{2} + 10 ) ^{\frac{2}{3}}}

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What is the derivative of f(x)=\sqrt[3]{36x^2+10} ?
The derivative of f(x)=\sqrt[3]{36x^2+10} is (24x)/((36x^2+10)^{2/3)}
What is the first derivative of f(x)=\sqrt[3]{36x^2+10} ?
The first derivative of f(x)=\sqrt[3]{36x^2+10} is (24x)/((36x^2+10)^{2/3)}