Calc 1 Formulas

Derivative power rule d/dx x^n

nx^n-1

Integration power rule ∫x^ndx

x^n+1/(n+1)+C, x cannot equal 1

product rule

f’g+g’f

quotient rule

f’g-g’f/(g)^2

f’ of sinx

cosx

f’ of cosx

-sinx

f’ of tanx

sec²x

f’ of cotx

-csc²x

f’ of secx

secx*tanx

f’ of cscx

-cscx*cotx

∫sinxdx

-cosx+C

∫cosxdx

sinx+C

∫tanxdx

ln|secx|+C

∫sec^²xdx

tanx+C

∫cotdx

ln|sinx|+C

∫csc²xdx

-cotx+C

∫secxdx

ln|secx+tanx|+C

∫secxtanxdx

secx+C

∫cscxdx

ln|cscx-cotx|+C

∫cscxcotxdx

-cscx+C

f’ of sin^-1x

1/(1-x²)^1/2

f’ of cos^-1x

1/(1-x²)^1/2

f’ of tan^-1x

1/(1+x²)

f’ of cot^-1x

-1(1+x²)

f’ of sec^-1x

1/(|x|(x²-1)^1/2)

f’ of csc^-1x

-1/(|x|(x²-1)^1/2)

∫du/((a²-u²)^1/2)

sin^-1u/|a|+C

∫du/(a²+u²)

1/atan^-1u/a+C

du/(u(u²-a²)^1/2

1/|a|sec^-1u/|a|+C

f’ of e^x

e^x

∫e^x

e^x+C

f’ of b^x

lnb(b^x)

∫b^xdx

b^x/lnb+C

f’ of lnx

1/x

∫1/xdx

ln|x|+C

f’ of logb|x}

1/(lnb)x

∫ -du/(a²-u²)^1/2

cos^-1u/|a|+C

∫ -du/a²+u²

1/acot^-1u/a+C

∫ -du/u(u²-a²)^1/2

1/|a|csc^-1u/|a|+C

∫ a^xdx

a^x/lna+C

∫ lnxdx

x(lnx-1)+C

∫ logaxdx

(x/lna)(lnx-1)+C