CAB-Chp-5ishA-NTsampASN2 - CalcAB Chp 5ishA Introduction to...

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CalcAB Chp 5ishA Introduction to Anti-derivatives NOTES 1. Before talk about anti-derivatives need to talk about another kind of derivative called DIFFERENTIAL derivative. Differential derivatives are similar to implicit differentiation. Implicit differentiation works derivative of a variable with respect to some variable; multiplies by rates like dy/dx, dA/dt, dx/dt, kind of thing. Differential derivatives do not involve rates, do not use “with respect to” designation. The differential derivative multiplies by “dx” for terms involving variable x, or multiplies “dy” for terms involving variable y, or multiplies by "du" for terms involving variable u, or, etc. Find the differential dy. Ex(c) Find differential dP. (a) y = 3x 4 (b) (c) P = 4q 2 + q <answers> (a) dy = 12x 3 dx (b) dy = dx (c) dP = (8q + 1) dq Why mention differential derivatives? Because they are part of the anti-derivative notation. 2. ANTI-DERIVATIVE undoes a derivative (work backwards) anti-derivatives do NOT have the same rules as derivatives (for ex, there are no product nor quotient rules for anti-derivative) ANTI-DERIVATIVE is a fairly new term for expressing:
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CAB-Chp-5ishA-NTsampASN2 - CalcAB Chp 5ishA Introduction to...

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