What is the derivative of \sqrt[3]{-3x^2+5x+1} ?

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (3 e^{x} + 8 x^{3} + 4 x) d x

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

x \to 0 - lim (h (x))

f (x) = ln (\frac{x ^{2}}{x ^{2} + 1})

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