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Popular >

derivative of sqrt(x*y)

Solution

\frac{d}{d x} (x \cdot y)

Solution

\frac{y + x \frac{d y}{d x}}{2 x y}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x y} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{2 x y}

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

Popular Examples

derivative of arctan(9/x+arctan(3/x))

\frac{d}{d x} (arctan (\frac{9}{x}) + arctan (\frac{3}{x}))

tangent of f(x)=(3x)/(x^2-2),\at x=1 tangent of

f (x) = \frac{3 x}{x ^{2} - 2}, at x = 1

integral of 1/(x(x+2)(x-3))

\int \frac{1}{x ( x + 2 ) ( x - 3 )} d x

integral from-infinity to 0 of 1/(3-5x)

\int_{- \infty}^{0} \frac{1}{3 - 5 x} d x

integral of (x^3+21)/(x^2+5x+6)

\int \frac{x ^{3} + 21}{x ^{2} + 5 x + 6} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x*y) ?
The derivative of sqrt(x*y) is (y+x\frac{dy)/(dx)}{2sqrt(xy)}
What is the first derivative of sqrt(x*y) ?
The first derivative of sqrt(x*y) is (y+x\frac{dy)/(dx)}{2sqrt(xy)}