What is the derivative of sqrt(x^3-4) ?

The derivative of sqrt(x^3-4) is (3x^2)/(2sqrt(x^3-4))

What is the first derivative of sqrt(x^3-4) ?

The first derivative of sqrt(x^3-4) is (3x^2)/(2sqrt(x^3-4))

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derivative of

x^{3} - 4

\frac{3 x ^{2}}{2 x ^{3} - 4}

Solution steps

\frac{d}{d x} (x^{3} - 4)

Apply the chain rule:

\frac{1}{2 x ^{3} - 4} \frac{d}{d x} (x^{3} - 4)

= \frac{1}{2 x ^{3} - 4} \frac{d}{d x} (x^{3} - 4)

\frac{d}{d x} (x^{3} - 4) = 3 x^{2}

= \frac{1}{2 x ^{3} - 4} \cdot 3 x^{2}

Simplify

\frac{1}{2 x ^{3} - 4} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} - 4}

= \frac{3 x ^{2}}{2 x ^{3} - 4}

\int e^{2 x y} d x

\int cos (2 x) cos (x) d x

\int \frac{x}{( x ^{4} + 1 )} d x

\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6}

What is the derivative of sqrt(x^3-4) ?
The derivative of sqrt(x^3-4) is (3x^2)/(2sqrt(x^3-4))
What is the first derivative of sqrt(x^3-4) ?
The first derivative of sqrt(x^3-4) is (3x^2)/(2sqrt(x^3-4))