calc exam

d/dx ( c )

0

d/dx [cf(x)]

f’(x)

d/dx (x^n)

nx^n-1

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

f’(x) + g’(x)

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

f’(x) - g’(x)

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

f ’(x) g(x) + g’(x) f(x)

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

f (x) g’ (x) - g (x) f ‘(x) / [g(x)]²

how to find tangent slope and equation of f(x)

find derivative f ‘ (x) and plug in given x value; plug result into y=mx+b to find line

how to find horizontal tangent values of x in f(x)

find f ‘ (x) and make it equal to zero to find values of x

limit def of derivative (difference quotient)

f(x+h) - f(x)/h

how to differentiate a limit

find the difference quotient using the limit definition, simplify, find the limit as h —> 0

when is a function NOT differentiable

when not continuous, has a corner or cusp, or vertical tangent

degrees to radians

degrees x radians/180

csc

1/sin

sec

1/cos

csc

cos/sin

aroc

f(b) - f(a)/b-a

y[logax] =

y’ = 1/x ln a

y[ln x ]

y’ = 1/x

y[ln u ]

(1/u)(y’u)

y[sin x ]

cos x

y[cos x ]

-sinx

y[tan x]

sec²x