bobsmith76 said:Homework Statement
∂f/∂x (xy -1)2 = 2y(xy-1)
The Attempt at a Solution
I would think the answer would be
2(xy-1)
I don't understand where the y comes from in 2y
The power rule states that the derivative of a variable raised to a power is equal to the power multiplied by the variable raised to the power minus one.
To apply the power rule to functions with multiple variables, you simply treat each variable as a constant and take the derivative with respect to the variable you are interested in. This is known as a partial derivative.
Yes, the power rule can be applied to find partial derivatives of non-polynomial functions as long as they can be written in the form of a variable raised to a power.
Partial derivatives are a special case of total derivatives. They represent the rate of change of a function with respect to one variable while holding all other variables constant.
The power rule can be used in real-world applications to calculate the rate of change of a quantity with respect to another quantity. For example, it can be used to find the marginal cost of production in economics or the rate of change of temperature with respect to time in physics.