math wa2 j1

a.b

|a||b|cosx

a.a

|a|²

a perpendicular to b

a.b=0

axb

|a||b|sinx

bxa

-(axb)

axa

0

a // b

axb=0, a=kb

perpendicular dist from A to OB (A is above OB)

AN=OAsinx=|axb|/|b|

length of projection of a onto b (a is above b)

ON=OAcosx=|a.b|/|b|

Area of triangle

½ |OA-OC|

d/dx a^x

a^x lna (for a^fx multiply by f’x)

d/dx e^x

e^x (multiply by f’x)

d/dx log a x

1/x . 1/lna

d/dx lnx

1/x (or f’x/fx)

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

sec² x

d/dx cscx

-cscxcotx

d/dx secx

secxtanx

d/dx cotx

csc²x

d/dx sin-1 x

1/sqrt (1-x²)

d/dx cos-1 x

-1/sqrt (1-x²)

d/dx tan-1 x

1/1+x²

graph of f’x

• vertical asy becomes y=0, horizontal asy same, oblique asy become y=gradient

• stationary pt (a,b) becomes x int (x=a)

• +ve gradient means curve above x axis, -ve is below

• concave upwards f’’x>0, concave downwards f’’x<0

~ e^(ax+b)

1/a . e^(ax+b)

~ ax

1/lna . a^x

~ 1/ax+b

1/a . ln|ax+b|

~ f’x(fx)^n

(fx)^n+1 / n+1

~ f’x .e^fx

e^fx

~ f’x/fx

ln|fx|

~ csc² (ax+b)

-1/a cot(ax+b)