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Popular >

derivative of sqrt(2xy)^3

Solution

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

Solution

32 x (y + x \frac{d y}{d x}) y

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x y) = \frac{y + x \frac{d y}{d x}}{2 x y}

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

Simplify

3 (2 x y)^{2} \frac{y + x \frac{d y}{d x}}{2 x y} : 32 x (y + x \frac{d y}{d x}) y

= 32 x (y + x \frac{d y}{d x}) y

Popular Examples

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n = 0 \sum \infty \frac{1}{2 ^{n}}

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\frac{d}{d x} ((x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5))

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f (x) = x^{2} - 11 y^{2}

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Frequently Asked Questions (FAQ)

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