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

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

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

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

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derivative of

3 x^{2} - 3

\frac{2 x}{3 ( x ^{2} - 3 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{5}^{7} x d x

\int_{- 1}^{1} 1 - ∣ x ∣ d x

\int 2 e^{2 t} d t

x \cdot y^{^{''}} + y^{^{'}} = 0

e^{x} 2

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