Basic Differentian Rules *with u and v

Calc AB/BC

D/dx {u±v}

D/dx {u±v}

d/dx u +d/dx v

d/dx c

0

d/x cu

c (u’)

d/dx (x)

1

d/dx (uⁿ)

nu^n-1(u’)

d/dx (uv)

u(v’)+v(u’)

d/dx [f(g(x))]

f’(g(x)) times g’(x)

d/dx lnu

1/u (u’)

d/dx [log_au]

1/u(lna) times u’

e^u

e^u (u’)

d/dx a^u

a^u (lna (u’))

sinu

cosu (u’)

cosu

-sinu (u’)

secu

secutanu (u’)

cscu

-cscucotu (u’)

tanu

sec²u (u’)

cotu

-csc²u(u’)

arcsinu

1/√ of (1-u²) * u’

arccosu

-1/√(1-u²) *(u’)

arcsecu

1/ |u| √(u²-1) * u’

d/dx arccsc

-1 / (|u|√(u² - 1)) * (du/dx)

d/dx arctanu

1/ 1+u² (u’)

arccotu

-1/(1+u²) (u’)

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

1/f’(f^-1(x)

dy/dx when in parametric

(dy/dt)/(dx/dt)

d²y/dx² when in parametric

(d/dt(dy/dx)) / (dx/dt)