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Popular Calculus >

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

area x^3-10x^2+16x,-x^3+10x^2-16x

a re a x^{3} - 10 x^{2} + 16 x, - x^{3} + 10 x^{2} - 16 x

derivative of (x^2-5x+3(4x^3+10x-5))

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

extreme f(x)=sqrt(x^2-11y^2)

e x t re m e f (x) = x^{2} - 11 y^{2}

derivative of 2x+3y

d er i v a t i v e 2 x + 3 y

integral from-2 to-1 of (x^2-x-2)

\int_{- 2}^{- 1} (x^{2} - x - 2) d x

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)