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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{5}{x}

\int 10 x^{\frac{3}{2}} d x

\int (e^{- x} - e^{2}) \cdot (e^{x} + e^{- 5}) d x

\int_{0}^{1} 3^{- x} d x

x \to - \infty lim (x^{2} - 3)

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