General Derivative FormulaConstant Function Linear Function Power RuleExamplesExercisesMAT 210 4.3 Slope (Derivative) FormulasGeneral Derivative FormulaIf xfy , then hxfhxfdxdyh 0limConstant Function Linear Function Power RuleIf by , then 0dxdyIf baxy , then adxdyIf nxy , then1nnxdxdyGeneral Exponential Function Particular Exponential Function Natural LogarithmIf xby , then bbdxdyxlnIf xey , then xedxdyIf xy ln, then xdxdy 1Examples1. Find the derivative of xxy 22 by using the general derivative formula. 2222lim22lim2222lim22limlim02022202200xhxhhhxhhxxhxhxhxhxxhxhxhxfhxfdxdyhhhhh2. Find the derivatives of the following functions using the formulas.a)xy 34 b) 3xy c) xxy 2d) xy 23dxdy 23xdxdy 12 xdxdy 2ln2xdxdye) xey f) xy ln g) 3224 xxxy xedxdy xdxdy 1 2322 xxdxdyExercises on the next page!Exercises1. Find the derivative of 232 xxy by using the general derivative formula.2. Find the derivative of the following using the derivative formulas.a)xy 54 b) 2yc) 5xy d) xy 4e) xxy lnf) 5423 xxyg) 26xxy h) xy i) 21xy j) 53 xyk) 43542 xxy l) xy1m) 33 xyxn)
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