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# Cal note card - 1 =f 1(g(x)g 1(x Derivative Using the...

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f(x)=14 If f(x)=c, the f 1 (x)=0 y=x 4 If f(x)=x n , the f 1 (x)=nx n-1 {Power Rule} g(x)=5x 3 If g(x)=cf(x), then g 1 (x)=cf 1 (x) y=3x 2 +4x If f(x)=u(x)+v(x), then f 1 (x)=u 1 (x)+v 1 (x) y=(x 2 -2)(x+4) If f(x)=u(x)∙v(x), then f 1 (x)= u(x)∙v 1 (x)+v(x)∙u 1 (x) {Product Rule} f(x)= x 3 _ x 2 +1 If f(x)=u(x) then f 1 (x)=v(x)∙u 1 (x)-u(x)∙v 1 (x) {Quotient Rule} v(x) [v(x)] 2 y=(x 3 -4x) 10 If y=u n and u=g(x), then dy = nu n-1 ∙ du dx dx y=(x-1) 3 (x 2 +3) 3 Power Rule, then Quotient Rule to find du where u =x -1 dx x 2 +3 y=(x+1)√(x 3 +1) Product Rule, then Power Rule to find v 1 (x), where v(x)= √(x 3 +1) y=(x 2 -3) 4 x+1 Quotient Rule, then Power Rule to find the derivative of the numerator. Log Function: y=log a x to a y =x lnx means log e x Chain Rule: If y=f(g(x)), then y
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Unformatted text preview: 1 =f 1 (g(x))g 1 (x) Derivative Using the Definition: 1.) Let h represent the change in x from x to x+h. 2.) The corresponding change in y=f(x) is f(x+h)-f(x). 3.) Form the difference quotient f(x+h)-f(x) and simplify. h 4.) Find lim f(x+h)-f(x) to determine f 1 (x). h→0 h f.y.i.:(x+h) 2 =(x 2 +2xh+h 2 ) Horizontal Tangents: x 2 +x-n=0→(x±a)(x±b)=0 Tangent Line: 1.) Evaluate to find (x,y) 2.) Evaluate the der. of f(x) to find slope(m). 3.) Use y-y 1 =m(x-x 1 ) with point (x,y) and slope(m). Determining Continuity: 1.) f(c) exists 2.) lim f(x) exists x→c 3.) #1 = #2...
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