Derivative Flashcards
π
0
x
1
f(x) = 2x^3 - 5x^2 +3x -2
6x^2 - 10x +3
f(x)g(x)
f’(x)g(x) + f(x)g’(x)
f(x)/g(x)
(f’(x)g(x) - f(x)g’(x)) / (g(x)^2)
f(x)^u
u(f(x)^u-1)(u’)
Sinx
Cosx
Cosx
-sinx
Sin^2(x)
f(x) = (sinx)^2
f’(x) = 2sinxcosx
√u
(1/2)u^(-1/2) u’
e^u
(e^u) u’
a^u
ln(a) (a^u) u’
loga^u
(1/ u ln(a)) u’
tanx
sec^2(x)
csc(x)
-csc(x)cot(x)
sec(x)
sec(x)tan(x)
cot(x)
-csc^2(x)
ln(u)
(1/u) u’
ln(u)
(1/u) u’
f(x) using a limit
(Lim h->0) (f(x-h) - f(x)) / h
sin^-1(x)
1/√(1-x^2)
cos^-1(x)
-1/√(1-x^2)
tan^-1(x)
1/(1+ x^2)
cot^-1(x)
-1/(1+ x^2)
csc^-1(x)
-1/(x√((x^2) -1))
sec^-1(x)
1/(x√((x^2) -1))
When to use squeeze theory
With trig
example: -1 < sinx < 1
|a| > x
-x > a > x
When to use l`hospital rule
0/0 or (+/-infinite)/(+/-infinite)
(d/dx)y^2 = (d/dx)x + (d/dx)5
(dy/dx)y = 1 + 0
L’hospital equation
(Lim x->a) f(x)/g(x) = (Lim x->a) f’(x)/g’(x)
L’hospital equation
(Lim x->a) f(x)/g(x) = (Lim x->a) f’(x)/g’(x)
