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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\frac{d}{d 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}

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

\frac{\partial}{\partial x} (4 π^{2} \frac{y}{x ^{2}})

arctan (2 x)

x \to 0 lim (\frac{2 x}{0})

e^{x}, x, 0, 2

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))