Math 150 SI Derivative Rules & examples by Kerrin Twigg https://padlet.com/kerrin2/gearmkkvo9d8fpbk First, fill in the rule/formula/process for each of the sticky notes. You can type or add a drawing. I will put you in BORs to add examples and solutions. en-us 2021-03-11 21:46:01 UTC 2024-07-25 14:51:31 UTC hello@padlet.com Implicit Differentiation - room 7 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300393089 Rule/Process: Put dy/dx to one side


Example: 
2x-y = -3
d/dx (2x-y) = d/dx(-3)
2 - 1(dy/dx) = 0
-dy/dx = -2
dy/dx = 2

]]> 2021-03-11 21:48:06 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300393089 Chain Rule - room 6 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300394896 Rule/Process: f'(g(x))g'(x)


Example: y = (x^3-1)^100
y' = d/dx [(x^3 -1)]^100
= 100(x^3-1)^99 * d/dx[x^3-1]
= 100(x^3-1)^99 * (3x^2)]]> 2021-03-11 21:48:42 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300394896 Product Rule - room 4 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300395489 Rule/Process:
f'g + g'f

Example: 
5x*x^2
(5x)(2x) + (5)(2x)]]> 2021-03-11 21:48:56 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300395489 Quotient Rule kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300395973 Rule/Process: If f(x) = h/g then f'(x) is,
(g(x)*h'(x)-h(x)*g('x))/(g(x))^2

Example: If f(x) = 2x/3x then f'(x) is,
(3x*2-2x*3)/(3x)^2]]> 2021-03-11 21:49:08 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300395973 Trig Derivatives kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300397460 d/dx sin(x)= cos(x)
d/dx cos(x)= -sin(x)
d/dx tan(x)= sec^2(x)
d/dx csc(x)= -csc(x)cot(x)
d/dx sec(x)= sec(x)tan(x)
d/dx cot(x)= -csc^2(x)

Trig Identities & their derivatives:
d/dx sinx = cosx
d/dx tanx = sec^2x
d/dx cosx = -sinx
d/dx cotx = -csc^2x
d/dx secx = secxtanx
d/dx cscx = -cscxcotx]]> 2021-03-11 21:49:44 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300397460 Derivatives of Logs & Exponents - room 5 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300401134 d/dx lnx = (1/x)
d/dx e^x = e^x
d/dx b^x = xb^(x-1)

ex: d/dx ln3x=3/3x=x]]> 2021-03-11 21:50:55 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300401134 Power Rule - room 3 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300415468 Rule/Process: if f(x)  = b^k then f'(x) is,
k*b^k-1


Example: if f(x)  = 2x^3 then f'(x) is,]]> 2021-03-11 21:56:20 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300415468 Limit Definition of a Derivative - room 2 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300417804 Rule/formula: lim h--->0 f(x+h)-f(x)/h]]> 2021-03-11 21:57:19 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300417804 Constant Multiple Rule - room 1 kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300420837 Rule/Process: d/dx cf(x) = cf'(x)

Example: 
5x^2 = 5(2x) = 10x]]> 2021-03-11 21:58:25 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1300420837 Related Rates kerrin2 https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1322115415 Rule/Process/steps: 
1: Identify Goal
2: Draw picture and identify knowns
3: Identify equation that connects the rates given and goal
4: Differentiate equation
5: Identify needed variables and solve for them if needed
6: isolate goal with units and plug in values]]> 2021-03-17 18:09:14 UTC https://padlet.com/kerrin2/gearmkkvo9d8fpbk/wish/1322115415