Implicit Differentiation and Derivatives

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What is Implicit Differentiation?

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Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y, rather than explicitly solving for y.

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What is the derivative of a constant?

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The derivative of a constant is 0.

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How do you differentiate a product of two functions?

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Use the product rule: if u and v are functions of x, then the derivative of uv is u'v + uv'.

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What is the Chain Rule in differentiation?

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The Chain Rule states that if a function y is composed of another function u, then the derivative of y with respect to x is dy/dx = dy/du * du/dx.

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What does dy/dx represent?

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dy/dx represents the derivative of y with respect to x, indicating the rate of change of y as x changes.

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What is the significance of the derivative in real-world applications?

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Derivatives are used to determine rates of change, such as speed, acceleration, and growth rates in various fields like physics, economics, and biology.

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