- #1
brambleberry
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Homework Statement
What is the deriv. of the square root of (xy)?
Homework Equations
The Attempt at a Solution
I used the chain rule:
(1/2)(xy)^(-1/2) times (y + x(dy/dx))
i am unsure on how to distribute this correctly
The derivative of the square root of xy is equal to (1/2)(x^(-1/2)y + x^(1/2)y^(-1)).
To find the derivative of the square root of xy, use the power rule and the chain rule. First, rewrite the expression as (xy)^1/2. Then, apply the power rule to get (1/2)(xy)^(-1/2). Finally, use the chain rule to multiply by the derivative of the inside function, which is (y + x). The final derivative is (1/2)(x^(-1/2)y + x^(1/2)y^(-1)).
Yes, the derivative of the square root of xy can be simplified using the power rule and the chain rule. The simplified form is (1/2)(x^(-1/2)y + x^(1/2)y^(-1)).
The derivative of the square root of xy represents the rate of change of this function with respect to its variables x and y. It can be used to find the slope of a tangent line at a specific point on the curve, as well as to determine maximum and minimum values of the function.
Yes, the derivative of the square root of xy has many real-life applications, particularly in physics and engineering. For example, it can be used to calculate the velocity of an object in projectile motion, or to determine the optimal dimensions of a structure given certain constraints.