Math Trig Identities, Derivatives, and Laws

sin

1/csc

cos

1/sec

tan

1/cot

csc

1/sin

sec

1/cos

cot

1/tan

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

sec²x

d/dx cotx

-csc²x

d/dx secx

secxtanx

d/dx cscx

-cscxcotx

lim (x—>0) tan(mx)/sin(nx)

m/n

lim (x—>0) sin(mx)/sin(nx)

m/n

lim (x—>0) tan(mx)/nx

m/n

when approaching 0, sin(mx) =

mx

lim (x—>0) sinx/x =

x

lim (x—>0) cosx -1 /x =

0

d/dx arcsinx

1/ sqrt(1-x²)

d/dx arccosx

-1/ sqrt(1-x²)

d/dx arctanx

1/(x²+1)

d/dx arccotx

-1/(x²+1)

d/dx arcsecx

1/ x sqrt(x²-1)

d/dx arccscx

-1/ x sqrt(x²-1)

d/dx (e^x)

e^x

d/dx (e^gx)

e^(gx) g’(x)

d/dx logb(x)

1/ xlnb

d/dx logb (gx)

g’x/ gxlnb

d/dx b^x

b^x lnb

d/dx b^gx

b^(gx) g’xlnb

d/dx lnx

1/x

linear approximation formula

Lx = f(a) + f’(a)(x-a)