Calculus Flashcards
Definition of Derivative
lim h->0 [F(x+h) - F(x)] / h
Product Rule
y = f(x)g(x)h(x) y’ = f’(x)g(x)h(x) + f(x)g’(x)h(x) + f(x)g(x)h’(x)
Quotient Rule
[(bottom)(top’) - (top)(bottom’)] / (bottom)²
Derivative y = sin(x)
y’ = cos(x)
Derivative y = cos(x)
y’ = -sin(x)
Derivative y = tan(x)
y’ = sec²(x)
Derivative y = sec(x)
y’ = sec(x)*tan(x)
Derivative y = cot(x)
y’ = -csc²(x)
Derivative y = csc(x)
y’ = -csc(x)*cot(x)
cos30º =
√3 / 2
tan30º =
√3 / 3
sin30º =
1/2
Derivative y = arcsin(x)
y’ = x¹ / (√1-x²)
Derivative y = arccos(x)
y’ = -x¹ / (√1-x²)
Derivative y = arctan(x)
y’ = x¹ / 1+x²
sinh(x) =
(e ͯ - eˉ ͯ) / 2
cosh(x) =
(e ͯ + eˉ ͯ) / 2
cos(A ± B) =
cosAcosB -+ sinAsinB =
sin(A ± B) =
sinAcoB -+ sinBcosA =
cos²θ + sin²θ =
1 =
sec²θ =
tan²θ + 1 =
csc²θ =
cot²θ + 1 =
Derivative sinh(x)
sinh(x)(x’)
Derivative tanh(x)
sech²(x)(x’)
Derivative sech(x)
-sech(x)*tanh(x)(x’)
Derivative cosh(x)
sinh(x)(x’)
Derivative csch(x)
-csc(c)*-coth(x)(x’)
Derivative coth(x)
-csch²(x)(x’)
Position vs. Velocity vs. Acceleration
s, s’ = ∆s/∆t, s’’ = ∆v/∆t = -32ft/sec
Average Value
1/b-a ∫ba f(x)dx
Log(a*b)
logA + logB
Log(a/b)
logA - logB
Sin2x =
2(cosx)(sinx)
Vertical Asymptotes
Set base to zero… F(x)
Logb ͯ =
xLogb
