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

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

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

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

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derivative of

x^{3} + 3

\frac{3 x ^{2}}{2 x ^{3} + 3}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{3} + 3} \cdot 3 x^{2}

Simplify

\frac{1}{2 x ^{3} + 3} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + 3}

= \frac{3 x ^{2}}{2 x ^{3} + 3}

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