Position functions and tangent lines
Using s(t)=t3+6t+8, what is the position of the particle at 2 seconds?
s(t)=28 inches
y=lnx, y'=
y'= 1/x (sometimes times k)
y=(2x/4x2)
y'=[-8x2/(4x2)2]
quotient rule
y=(x2+6x-3)+(x3-4)
y'=(2x+6)+(3x2)
power rule + addition rule
y=(6x2-5)4, y'=
y'=48x(6x2-5)3
Using s(t)=t3+6t+8, what is the average velocity of the particle from [ 1 , 3 ] ?
Average velocity: 21 in/s
y=sinx, y'=
g(x)=cosx, g(x)'=
y'=cosx
g(x)'=-sinx
f(x)=(3x2-1)/(2x+5)
f(x)=[2(3x2+15x+1)/(2x+5)2]
quotient rule
y=(1/4)ex+x4-2
y'=(1/4)ex+4x3
power rule and ex
y=(1/3x3+4)-1, y'=
y'=[-x/(1/3x3+4)2]
Using s(t)=t3+6t+8, what is the acceleration of the particle at 2 seconds?
12 in/s2
y=secx, y'=
g(x)=tanx, g(x)'=
y'=secx x tanx
g(x)'=sec2x
y=lnxcosx
y'=(cosx/x)-lnxsinx
product rule and trig/log functions
y=2x
y'=2x x ln2
y=ax -> ax x lna
y=3ln3x, y'=
y'=[9(3lnx)3/x]
Using s(t)=t3+6t+8, find the acceleration of the particle when its velocity is 33 in/s.
18 in/s2
y=cscx, y'=
g(x)=cotx, g(x)'=
y'=-cscx x cotx
g(x)'=-csc2x
f(x)=square root of x(1-x2)
f(x)'=[(-5x2-1)/(2 times the square root of x)
f(x)=16[(x3-2x2)-(4x4+6x5-3)]
f(x)'=16[(3x2-4x)-(16x3+30x4)]
power rule, subtraction rule and constant rule
y=e(x^2+3x), y'=
y'=e(x^2+3x) x (2x+3)
Find Ltan:f(x)=4x3+ex-sinx; x=3
round to four decimal places
Ltan: y=129.0755x-1.1311
y=logax, y'=
y'=1/x(lna)
g(x)=2x(3cosx)
g(x)'=(2x x ln2 x 3cosx)+(-3sinx x 2x)
product rule, ax, and trig/log functions
y=xe
y'=exe-1
the 'e' trick
y=csc(2 root x), y'=
y'=-csc(2 root x) x cot(2 root x) x x-1/2