Final Exam.. gulp Flashcards
Power rule
u^v=vu^v-1
Product rule
u*v=u’v+v’u
Quotient rule
u/v=u’v-v’u/(v)^2
Chain rule
u^n=nu^n-1*u’
(a+b)/c can be rewritten as..
a/c+b/c
a^g/x^b can be rewritten as
ax^(g-b)
when doing implicit differentiation and you have y raised to a power
use the chain rule
when finding a limit if you substitute x and it = 0, you must
factor first then plug in
how to find the integral of x^ndx
(x^(n+1)/n+1)+C
finding tangent/normal line when a value is given (instead of there being y)
use implicit differention
1) find derivative of each term
2) isolate terms w/out y’, factor out y’, and isolate y’
3) plug in (x, y) to get tangent, the reciprocal is normal
4) plug into y-y1=m(x-x1) to get equation
Find the extreme/relative values
1) find F’(x)
2) set F’(x)=0 to get critical numbers
3) list intervals using from step 2
4) take test values (values between each interval)
5) plug the test value in f’(x)
6) if positive, the interval is increasing, if negative the interval is decreasing
7) create a timeline marking the critical numbers
8) if there is mountain, it is relative max at this x, if there is valley, there is relative min at this x
9) plug the relative values into f(x) to get their y values
finding tangent/normal line when a value is not given (y=)
1) find y by plugging in x to equation
2) find y’
3) plug in x to get tangent
4) plug into y-y1=m(x-x1) to get equation
finding integral of f(x) raised to n
1) put any coeff. in front of ∫
2) find du by taking derivative of u (what’s in the parenthesis)
3) use formula u^ndu= (u^n+1)/n+1+C
To find definite integral
1) find the integral
2) set up using the formula F(b)-F(a), substituting x (b is the top value)
3) simplify
Integral of sinx
-cosx
