calculus u3

d/dx (sinx) =

cosx

d/dx (tanx) =

sec²x

d/dx (cosx) =

-sinx

d/dx (cscx) =

-cscxcotx

d/dx (cotx) =

-csc²x

d/dx (a^x) =

(ln a) a^x

d/dx (ln x) =

1/x

d/dx (log_bx) =

(1/ln b)(1/x)

d/dx (secx) =

secxtanx

limit definition of derivative

lim_h→0 ( f(x+h) - f(x) ) / h

lim_x→a ( f(x) - f(a) ) / x-a

g(x)=f’(x)

g’(x)=1/f’(g(x))

f(g(x))=x means…

inverse

d/dx(f(g(x)) aka composite function =

f’(g(x))·g’(x)

d/dx(e^u)

e^u·du/dx

d/dx(a^u)=

a^u·(ln a)du/dx

d/dx(ln u)=

1/u · du/dx

d/dx(log_bu)=

1/u · 1/ln b · du/dx

d/dx(sin^-1x)=

1/(√1-x²)

d/dx(sin u)=

cos u · du/dx

d/dx(sin^-1u)=

1/(√1-u²) · du/dx

d/dx(tan^-1u)=

1/(1+u²) · du/dx

d/dx(cos^-1u)=

-1/(√1-u²) · du/dx

d/dx(sec^-1u)=

1/(|u|√u²-1) · du/dx