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

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

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

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

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derivative of

f (x) = 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}

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\int \frac{1}{441 - 400 x ^{2}} d x

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