Calculus Review

Derivative Formulas

100

d/du[lnu] = ?

u'/u

200

d/du[e^u] = ?

e^u 

300

d/dx[a^x] = ?

(a^x)(lna)

400

d/dx[log_ax] = ?

1/(xlna)

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

∫e^2xdx = ?

1/2 e^2x + C

400

∫1/x³ dx = ?

-1/2 x^-2 + 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|secu| + C

or -ln|cosu| + C

300

∫cotu du

-ln|cscu| + C

or ln|sinu| + C

400

∫secu du = ?

ln|secu + tanu| + C

500

∫cscu du = ?

-ln|cscu + cotu| + C

Miscellanious

100

This point is found where f" changes signs

Point of Inflection

200

This formula is used for total distance traveled

Integral from a to b of |v(t)|

300

This is the limit as x approaches infinity of (2x⁴+3x)/(5x⁴+x)

2/5

400

This is what f' is doing when f is concave down

Decreasing

500

d/dx [3sin²(5x)] = ?

30sin(5x)cos(5x)