Calculus Review

Derivative Formulas

100

d/du[lnu] = ?

u'/u

200

d/du[e^u] = ?

e^u du/dx

300

d/dx[arctanu] = ?

u'/(1+u²)

400

d/dx[log_au] = ?

1/(lna * u) * du/dx

500

(f^-1)'(x) = ?

1/[f'(f^-1(x))]

Antiderivative Formulas

100

∫e^u du = ?

e^u + C

200

∫1/u du = ?

ln|u| + C

300

∫du/(sqrt(a²-u²)) = ?

arcsin(u/a) + C

400

∫du/(a² + u²) = ?

(1/a)arctan(u/a) + C

500

∫a^x dx = ?

(1/lna) * a^x + C

Trig Derivatives

100

d/dx[sinx] = ?

d/dx[cosx] = ?

cosx

-sinx

200

d/dx[tanx] = ?

sec²x

300

d/dx[cotx] = ?

-csc²x

400

d/dx[secx] = ?

secx * tanx

500

d/dx[cscx] = ?

-cscx * cotx

Trig Antiderivatives

100

∫sinu du

∫cosu du

-cosu + C

sinu + C

200

∫tanu du

-ln|cosu| + C

300

∫cotu du

ln|sinu| + C

400

∫secu du = ?

ln|secu + tanu| + C

500

∫cscu du = ?

-ln|cscu + cotu| + C