Math Problem Statement
dxdy=2x−1 derivative
Solution
To find the derivative of the equation , we can follow these steps:
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Interpret the equation: We have , which means we are taking the derivative of with respect to . The right-hand side is .
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Differentiate implicitly: Since is a function of , we need to differentiate both sides with respect to , applying the chain rule to .
Differentiating with respect to will give , and differentiating the right side gives:
Therefore, the equation becomes:
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Solve for :
Simplifying:
Multiply both sides by :
Thus, the derivative of with respect to is:
Do you want a more detailed explanation or have any further questions?
Here are 5 related questions to explore further:
- How would you solve for from ?
- What does the equation represent in terms of a differential equation?
- How do you apply implicit differentiation to other equations?
- What is the role of the chain rule in this differentiation process?
- How can this result be interpreted graphically?
Tip: When performing implicit differentiation, always remember to treat any variables (like in this case) that are functions of the other variable (here ) using the chain rule.
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Derivatives
Chain Rule
Formulas
d/dy(2x - 1) = 2 * dx/dy
Theorems
Implicit Differentiation
Chain Rule
Suitable Grade Level
Grades 11-12