Calculus Midterm Flashcards
d/dx (cosu)
-(sinu) u’
d/dx (cos (kx))
-ksin(kx)
d/dx (tanx)
sec^2(x)
d/dx (tanu)
(sec^2u) u’
d/dx (cot (x)
-csc^2 x
d/dx (cotu)
-(csc^2u)u’
d/dx (sin(x))
cosx
d/dx (sin(u))
(cosu)u’
d/dx (sin(kx))
kcos(kx)
d/dx (cosx)
-sinx
d/dx (secx)
secxtanx
d/dx (secu)
(secutanu) u’
d/dx (cscx)
-cscxcotx
d/dx (cscu)
-(cscucotu)u’
Factor theorem
If P(x) is a polynomial and P(a)=0 then x-a is a factor of P(x)
a/b - c/d
(ad-bc)/bd
When direct substitution in a limit results in a nonzero number/zero
limit is either +infinity or -infinity or does not exist.
sin(0)
0
cos (0)
1
sin (pi/2)
1
Power Rule
d/dx x^n = nx^n-1
Definition of a derivative
lim h->0 f(x+h)-f(x)/h
Derivative of a sum
(f + g)’ = f’ + g’
Chain rule
d/dx f(g(x)) = f’(g(x)) g’(x)
Exponential Derivative
d/dx (e^x) = e^x)
Exponential derivative chain rule
d/dx (e^u) = (e^u)u’
Exponential derivative special case
d/dx e^kx = ke^kx
Log Derivative
d/dx ln(x) = 1/x
log derivative chain rule form
d/dx ln(u) = u’/u
product rule
d/dx (fg) = f’g + fg’
ln (1)
0
ln(e)
0
