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2.5 Implicit Differentiation
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Implicit DIfferentiation
Previous rules such as the product, quotient, power, and chain were only able to be applied to functions written in explicit form. Explicit form is when y is written as a function of x. When a function is not written explicitly you can either change the function to explicit form or use implicit differentiation. Explicit Form y = 1/x Implicit Form xy =1
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2.5 Implicit Differentiation
Solve for y
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2.5 Implicit Differentiation
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Take the derivative of each term, with respect to x
Bring the dy/dx terms left, all other terms right. Factor out and solve for dy/dx. Slope
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2.5 Implicit Differentiation
Can't solve for y... So solve for x. Graph it... Slope
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Always use this Tstep
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Derivative
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2.5 Implicit Differentiation
Degenerate Circle
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2.5 Implicit Differentiation
Unit Circle Vertical Tangents
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2.5 Implicit Differentiation
Solve for y... ?
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2.5 Implicit Differentiation
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2.5 Implicit Differentiation
Not in terms of x implies chain rule
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2.5 Implicit Differentiation
Rotate 90 degrees Parametric Mode Reflect over y
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2.5 Implicit Differentiation
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2.5 Implicit Differentiation
2.5/3,5,7,11,13,15,19,21,24,25,29,32,35,38,41,45,49,53,57
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