- #1
oswald
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Homework Statement
Finda dw/dt
w=3xy/x²-y²
x=t3
y=e2t
Homework Equations
w=(3t3e2t)/(t6-e4t)
The Attempt at a Solution
Well,is there anothe way to solve this, instead of dw/dt; like dw/dx * dw/dt + dw/dy * dy/dt ?
A derivative is a mathematical concept that represents the rate of change of a function with respect to its input. It measures how much a function is changing at a specific point.
Calculating the derivative of w with respect to t is important because it allows us to understand the rate of change of w with respect to t. This is useful in many fields, such as physics, economics, and engineering, as it allows us to make predictions and analyze the behavior of a system.
To calculate the derivative of w with respect to t, we use the rules of calculus, specifically the chain rule and the product rule. We take the derivative of each term in the function and combine them using these rules to find the overall derivative.
Calculating the derivative of w with respect to t is used in many real-world applications, such as calculating the velocity of an object at a specific time, determining the optimal production level in economics, and predicting the growth rate of a population.
The derivative of w with respect to t represents the slope of the tangent line to the graph of w at a specific point. This means that the derivative tells us the rate of change of w at that point, which can be interpreted as the slope of the line that best approximates the curve at that point.