- #1
-EquinoX-
- 564
- 1
Homework Statement
What is the derivative of sqrt(xy) with respect to y?
Homework Equations
The Attempt at a Solution
The sqrt(xy) is equal as (xy)^(1/2), so therefore what I have is 1/2 (xy) ^ -1/2, why is this wrong?
The derivative of sqrt(xy) is 1/2 * (x^(-1/2)y + y^(-1/2)x).
To find the derivative of sqrt(xy), you can use the product rule and chain rule. First, take the derivative of sqrt(x) with respect to x, which is 1/2 * x^(-1/2). Then, take the derivative of y with respect to x, which is dy/dx. Finally, use the chain rule to multiply the two derivatives together.
Yes, the derivative of sqrt(xy) can be simplified to (1/2)sqrt(y/x) + (1/2)sqrt(x/y).
The domain of the derivative of sqrt(xy) is all real numbers except when x and y are both equal to 0.
Yes, the derivative of sqrt(xy) can be negative. The sign of the derivative depends on the values of x and y. If both x and y are positive, the derivative will be positive. If both x and y are negative, the derivative will be negative. If x and y have opposite signs, the derivative will be negative.