Limits 1
lim 1--->-1
DNE
lim x--->5
(x-3)(x+3)/(x-3)
8
Product Rule
y= (x^4+3)(-4x^5+5x^4+5)
find f'
y'=-36x^8+40x^7-60x^4+80x^3
Power Rule
4x^2+3x
find f'(5)
f'(5)=43
Trig
y=2xsinx+x^2cosx
find y'
y'=4xcosx+2sinx-x^2sinx
lim x---> 1
1
lim x ---> 6
(x-8)(x+8)/(x-8)
14
Product Rule
f(x)=(-3x+x^-3)(-4x^3+3)
find f'(x)
f'(x)=36x^6-24x^3-9/x^4
Chain Rule
y=(x^2+3x)^5
find f'
f'=5(x^2+3x)^4 x (2x+3)
Trig
y=3xcosx+x^3sinx
find y'
y'=-3xsinx+cosx+x^3cosx+3x^2sinx
lim x--->2
(x-2)(x+2)/(x-2)
4
Name the limit and solve
lim x---> - infinity
4x+8/5x
BETC 4/5
Product Rule
y=(-2x^4-3)(-2x^2+1)
find y'
y'=24x^5-8x^3+12x
Chain Rule
y= 1/(x^2-2x-8)^-3
find f'(x)
f'(x)=-3(x^2-2x-8)^-4(2x-2)
Higher Order
f(x)= -1/7x^-3-2/5x^6-1/5x-1/3x^3
find f''(x)
f''(x)=-12x^4-2x-2x^-5
lim x--->4
(2x-4)(x-2)/(x+4)
1
Name the limit and solve
lim x---> infinity
3-2x^2/3x-1
BOTU DNE
Power Rule
f(x)=-5x^3-2x^2+x+8
find f'(x)
f'(x)=-15x^2-4x+1
Chain Rule
y=sin(2x)
find y'
y'=2cos(2x)
Higher Order
y=3/8x^2+1/2x^4+2/3x^3+1/5x^5
find d^3y/dx^3
d^3y/dx^3=12x^2+12x+4
lim x--->6
(x^2+6)(6+2)/(x+8)
24
Name the limit and solve
lim x---> - infinity
3-2x/3x^3-1
BOBO 0
Power Rule
y=-2x^-4-6x^3
find y'
y'=8/x^5 -18x^2
Trig
f(x)=-x+secx
find f'(x)
f'(x)= -1+secxtanx
Higher Order
f(x)=5/7x-3/10x^6+2x^2
Find f''(x)
f''(x)=-9x^4+4