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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{e^{3}} \frac{ln ^{2} ( x ^{2} )}{x} d x

e^{t - 2}

f (t) = 3 e^{t}

\frac{d}{d x} (ln (1 - \frac{1}{x ^{2}}))

\frac{\partial}{\partial x} (a cos^{2} (2 π) (t - x))

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