Implicit Differentiation

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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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When is Implicit Differentiation used?

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Implicit differentiation is used when it is difficult or impossible to solve for y explicitly in terms of x.

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What is the derivative of a constant?

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The derivative of a constant is zero.

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How do you differentiate a product of functions using implicit differentiation?

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Use the product rule: if u and v are functions of x, then d(uv)/dx = u(dv/dx) + v(du/dx).

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What is the chain rule in implicit differentiation?

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The chain rule states that if y is a function of u, which is a function of x, then dy/dx = (dy/du)(du/dx).

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What is the slope of the tangent line?

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The slope of the tangent line at a point on a curve is the value of the derivative at that point.

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The slope is 9.

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