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  1. Limits and Derivatives Formulas 1. Limits Properties if lim ( ) x a f x l → = and lim ( ) x a g x m → =, then lim ( ) ( )[ ] x a f x g x l m → ± = ± lim ( ) ( )[ ] x a f x g x l m → ⋅ = ⋅ ( ) lim x a ( ) f x l → g x m = where m ≠ 0 lim ( ) x a c f x c l → ⋅ = ⋅ 1 1 lim x a→ f x l( ) = where l ≠ 0 Formulas 1 lim 1 n x ...

  2. Derivative Rules and Formulas Rules: (1) f 0(x) = lim h!0 f(x+h) f(x) h (2) d dx (c) = 0; c any constant (3) d dx (x) = 1 (4) d dx (xp) = pxp 1; p 6= 1 (5) d dx [f(x) g(x)] = f0(x) g0(x) (6) d dx (cf(x)) = cf0(x) (7) d dx [ f x)g)] = )+ (8) d dx f(x) g(x) = f0(x)g(x) f(x)g0(x) (g(x))2 (9) d dx 1 g(x) = g0(x) (g(x))2 (10) d dx [ f (g x))] = 0 ...

  3. Left hand limit : lim f ( x ) = L . This has the. x < a . except we require x large and negative. can make f ( x ) arbitrarily large (and positive) by taking x sufficiently close to a (on either side of a) without letting x = a . except we make f ( x ) arbitrarily large and negative. Note : sgn ( a ) = 1 if a > 0 and sgn ( a ) = - 1 if a < 0 .

  4. • Power Rule: f(x)=xn thenf0(x)=nxn−1 • Sum and Difference Rule: h(x)=f(x)±g(x)thenh0(x)=f0(x)±g0(x) • Product Rule: h(x)=f(x)g(x)thenh0(x)=f0(x)g(x)+f(x)g0(x) • Quotient Rule: h(x)= f(x) g(x) thenh0(x)= f0(x)g(x)−f(x)g0(x) g(x)2 • Chain Rule: h(x)=f(g(x))thenh0(x)=f0(g(x))g0(x) • Trig Derivatives: – f(x)=sin(x)thenf0(x)=cos(x)

  5. Symbolab Derivatives Cheat Sheet Derivative Rules: :Power Rule: 𝑑 𝑑𝑥 𝑥𝑎 ;=𝑎⋅𝑥𝑎−1 ;Derivative of a Constant: 𝑑 𝑑𝑥 :𝑎=0 2Sum/Difference Rule:

  6. 9 Δεκ 2022 · Having trouble remembering all of the different derivative rules? Check out this free printable derivatives formula chart I created for my AP Calculus students to use as a reference. It is available to download both as a PDF and WORD document.

  7. Implicit derivatives. (1) You start with an equation involving x’s, y’s, and/or numbers. (2) You take the derivative of both sides of the equation. When you do this you view y as a function of x and use the chain rule, product rule, etc. as needed. (For example d dx y2 = 2yy0, d dx sin( y) = cos( ) 0, d xy= + , etc..) (3) You solve the new ...

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