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

The derivative of \sqrt[3]{5x^2-3x+2} is (10x-3)/(3(5x^2-3x+2)^{2/3)}

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

The first derivative of \sqrt[3]{5x^2-3x+2} is (10x-3)/(3(5x^2-3x+2)^{2/3)}

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\frac{10 x - 3}{3 ( 5 x ^{2} - 3 x + 2 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2} - 3 x + 2) = 10 x - 3

= \frac{1}{3 ( 5 x ^{2} - 3 x + 2 ) ^{\frac{2}{3}}} (10 x - 3)

Simplify

\frac{1}{3 ( 5 x ^{2} - 3 x + 2 ) ^{\frac{2}{3}}} (10 x - 3) : \frac{10 x - 3}{3 ( 5 x ^{2} - 3 x + 2 ) ^{\frac{2}{3}}}

= \frac{10 x - 3}{3 ( 5 x ^{2} - 3 x + 2 ) ^{\frac{2}{3}}}

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What is the derivative of \sqrt[3]{5x^2-3x+2} ?
The derivative of \sqrt[3]{5x^2-3x+2} is (10x-3)/(3(5x^2-3x+2)^{2/3)}
What is the first derivative of \sqrt[3]{5x^2-3x+2} ?
The first derivative of \sqrt[3]{5x^2-3x+2} is (10x-3)/(3(5x^2-3x+2)^{2/3)}