What is the derivative of sqrt(x^3+8x) ?

The derivative of sqrt(x^3+8x) is (3x^2+8)/(2sqrt(x^3+8x))

What is the first derivative of sqrt(x^3+8x) ?

The first derivative of sqrt(x^3+8x) is (3x^2+8)/(2sqrt(x^3+8x))

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\frac{d}{d x} (x^{3} + 8 x)

\frac{3 x ^{2} + 8}{2 x ^{3} + 8 x}

Solution steps

\frac{d}{d x} (x^{3} + 8 x)

Apply the chain rule:

\frac{1}{2 x ^{3} + 8 x} \frac{d}{d x} (x^{3} + 8 x)

= \frac{1}{2 x ^{3} + 8 x} \frac{d}{d x} (x^{3} + 8 x)

\frac{d}{d x} (x^{3} + 8 x) = 3 x^{2} + 8

= \frac{1}{2 x ^{3} + 8 x} (3 x^{2} + 8)

Simplify

\frac{1}{2 x ^{3} + 8 x} (3 x^{2} + 8) : \frac{3 x ^{2} + 8}{2 x ^{3} + 8 x}

= \frac{3 x ^{2} + 8}{2 x ^{3} + 8 x}

f (x) = e^{2 y} (1 - y)

\frac{d}{d x} ((1 0^{x} + 1 0^{- x})^{2})

x \to 2 lim (\frac{4 x}{x - 2})

x^{2} - 8 x + 9

x^{2} - 2 x + 2, (0, 1)

What is the derivative of sqrt(x^3+8x) ?
The derivative of sqrt(x^3+8x) is (3x^2+8)/(2sqrt(x^3+8x))
What is the first derivative of sqrt(x^3+8x) ?
The first derivative of sqrt(x^3+8x) is (3x^2+8)/(2sqrt(x^3+8x))