midterm 2 Flashcards
Product rule [f(x)g(x)}
f(x)g’(x)+g(x)f’(x)
Quotient rule [f(x)/g(x)]
g(x)f’(x)-f(x)g’(x)/g(x)^2
Power rule [x^n]
nx^n-1
Difference rule [f(x)-g(x)]
f’(x)-g’(x)
Chain rule d/dx [f(g(x))]
f’(g(x))g’(x)
Constant multiple [g(x) = C*f(x)]
C*f’(x)
Sum rule [f(x)+g(x)]
f’(x)+g’(x)
sinx
cosx
cosx
-sinx
tanx
sec^2x
secx
secxtanx
cotx
-csc^2x
cscx
-cscxcotx
tanx (identity)
sinx/cosx
sin(ax)
acos(ax)
cos(ax)
-asin(ax)
a^x
ln(a)a^x
e^x
e^x
e^kx
ke^x
lnx
1/x
sin^-1x
1/sqrt(1-x^2)
cos^-1x
-1/sqrt(1-x^2)
tan^-1x
1/1+x^2
cot^-1x
-1/1+x^2
sec^-1x
1/xsqrt(x^2-1)
csc^-1x
-1/xsqrt(x^2-1)
How do you find critical numbers?
set f’(x) = 0 and solve
how do you find where f(x) is increasing/decreasing?
evaluate f’(x) at intervals
how do you find inflection points?
set f’‘(x) = 0 and solve
How do you find relative extrema?
evaluate f(x) at increasing and decreasing intervals
how do you find absolute extrema?
evaluate f(x) at all intervals
l’Hospitals rule
if f(x)/g(x) = 0/0 or oo/oo the f’(x)/g’(x)
how do you find delta x?
b-a/n
What is the derivative of position?
velocity
What is the derivative of velocity?
acceleration
