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Popular >

derivative of sqrt(x)(x^3+8)

Solution

derivative of

x (x^{3} + 8)

Solution

\frac{7 x ^{3} + 8}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{3} + 8

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

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

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

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

Simplify

\frac{1}{2 x} (x^{3} + 8) + 3 x^{2} x : \frac{7 x ^{3} + 8}{2 x}

= \frac{7 x ^{3} + 8}{2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x^3+8) ?
The derivative of sqrt(x)(x^3+8) is (7x^3+8)/(2sqrt(x))
What is the first derivative of sqrt(x)(x^3+8) ?
The first derivative of sqrt(x)(x^3+8) is (7x^3+8)/(2sqrt(x))