Multivariate Calculus Chain Rule.

[jaguar7]

Homework Statement

Apply the two cases of th change rule. For example: The voltage V in an electrical circuit is slowly decreasing as a battery wears out and the resistance R is slowly increasing as the resistor heats up Use Ohm's law V=IR to find how the current is changing (with respect to time) at the instant that R = 400 ohms, I = 0.08A, dV/dt = -0.01V/s, and dR/dt = .03 ohms/s. (Answ: -3.1 * 10^(-5)A/s)

Homework Equations

I guess we have three variables, V, I, and R. Do we use the multiplication rule and get (dV/dt = R dI/dt + I dR/dt) ?

The Attempt at a Solution

 

[Mark44]

Homework Statement

Apply the two cases of th change rule. For example: The voltage V in an electrical circuit is slowly decreasing as a battery wears out and the resistance R is slowly increasing as the resistor heats up Use Ohm's law V=IR to find how the current is changing (with respect to time) at the instant that R = 400 ohms, I = 0.08A, dV/dt = -0.01V/s, and dR/dt = .03 ohms/s. (Answ: -3.1 * 10^(-5)A/s)

Homework Equations

I guess we have three variables, V, I, and R. Do we use the multiplication rule and get (dV/dt = R dI/dt + I dR/dt) ?

Sure. Solve this equation for dI/dt, and evaluate it for the given values of I, R, dV/dt, and dR/dt.