What is the derivative of sqrt(x^3+5) ?

The derivative of sqrt(x^3+5) is (3x^2)/(2sqrt(x^3+5))

What is the first derivative of sqrt(x^3+5) ?

The first derivative of sqrt(x^3+5) is (3x^2)/(2sqrt(x^3+5))

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\frac{d}{d x} (x^{3} + 5)

\frac{3 x ^{2}}{2 x ^{3} + 5}

Solution steps

\frac{d}{d x} (x^{3} + 5)

Apply the chain rule:

\frac{1}{2 x ^{3} + 5} \frac{d}{d x} (x^{3} + 5)

= \frac{1}{2 x ^{3} + 5} \frac{d}{d x} (x^{3} + 5)

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

= \frac{1}{2 x ^{3} + 5} \cdot 3 x^{2}

Simplify

\frac{1}{2 x ^{3} + 5} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + 5}

= \frac{3 x ^{2}}{2 x ^{3} + 5}

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\int \frac{- 7}{x ^{2} + 16} d x

x \to 5 lim (\frac{( ln ( \frac{x}{5} ) )}{x ^{2} - 25})

\int \frac{1}{ln ( x ^{x} )} d x

\int \frac{x}{12} d x

What is the derivative of sqrt(x^3+5) ?
The derivative of sqrt(x^3+5) is (3x^2)/(2sqrt(x^3+5))
What is the first derivative of sqrt(x^3+5) ?
The first derivative of sqrt(x^3+5) is (3x^2)/(2sqrt(x^3+5))