The notation dx/dt represents the derivative of x with respect to t. It measures the rate at which x is changing with respect to time.
Think of dx/dt as a speedometer in a car. Just like a speedometer tells you how fast your car is going, dx/dt tells you how fast x is changing over time.
Derivative: The derivative of a function measures its rate of change at any given point.
Rate of Change: Rate of change refers to how much one quantity changes in relation to another quantity.
Instantaneous Rate of Change: Instantaneous rate of change describes the rate at which a function is changing at a specific point.
A particle moves on the xy-plane. The following equations about the particle’s movement are true: dy/dx = 4t^2 - 1 and dx/dt = t. Find y(t) given that y(0) is 25.
A particle moves on the xy-plane. The following equations about the particle’s movement are true: dy^2/dx^2 = 2t^4 + 6t^2 + 3t and dx/dt = 1/t. Find y(t) given that y(0) is 25.
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