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Popular >

derivative of sqrt(x)(x^2+8)

Solution

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

Solution

\frac{5 x ^{2} + 8}{2 x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + 8

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

\frac{1}{2 x} (x^{2} + 8) + 2 x x : \frac{5 x ^{2} + 8}{2 x}

= \frac{5 x ^{2} + 8}{2 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x^2+8) ?
The derivative of sqrt(x)(x^2+8) is (5x^2+8)/(2sqrt(x))
What is the first derivative of sqrt(x)(x^2+8) ?
The first derivative of sqrt(x)(x^2+8) is (5x^2+8)/(2sqrt(x))