Chain Rule
y=(x3+3)5
15x2(x3+3)4
find derivative of
f(x)= 3/2x2
3x
∫-9 dx
-9x + c
∫(3cosx)/5 dx
(3sinx)/5 + c
A function that is differentiable is always...
y=(5x2+3)4
40x(5x2+3)3
find derivative of
f(x)= ln(x3+3x2+7)
(3x2+6x)/(x3+3x2+7)
∫14x dx
7x2 + c
f(x)= tan(3x)
3sec2(3x)
How do you find acceleration when given position formula?
Find the second derivative
y=(-x4-3)-2
(8x3)/(-x4-3)3
find derivative of
f(x)= 6x4-4x3+12x2-17
24x3-12x2+24x
∫x7 dx
x8/8 + c
find derivative of
f(x)= (sin(4x))7
28sin(4x)6(cos(4x))
What law is used when a limit equals 0/0?
L'Hopital's Rule
y=(-5x3-3)3
-45x2(-5x3-3)2
f(x)= 16x1/2-2x4
(32/x1/2)-8x3
∫3x3 dx
3x4/4 + c
What is the inverse trig function of tan(x)?
(1)/(1+x2)
___________ states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]
Mean Value Theorem
y=((2x+5)5-1)4
40((2x+5)5-1)3(2x+5)4
find the derivative of
f(x)= 4x5-12x+87986647646587
20x4-12
∫x4-x2+3 dx
x5/5 + x3/3 +3x + c
∫7/(x2+1)
7tan-1(x)+c
The greatest calc teacher of all time
Who is Mrs. Vasquez?