differential calculus flashcard test

the secant line

the average rate of change between a and b is the slope of..

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

secant line equation

the tangent line

the instantaneous rate of change at x=a is the slope of…

f prime of a

equation of the slope of the tangent line

perpendicular to the tangent line

the normal line to a curve is…

opposite reciprocal of the slope of the tangent line

the slope of the normal line is…

false

true or false? if a function is continuous, it is differentiable

true

true or false? if a function is differentiable, then it is continuous

f prime plus or minus g prime

prime of (f plus or minus g)

(f times g prime) + (f prime times g)

f times g prime

(lowdhigh - highdlow) / low²

(f/g) prime

cos x

prime of sin x

-sin x

prime of cos x

sec² x

prime of tan x

sec x tan x

prime of sec x

-csc x cot x

prime of csc x

-csc²x

prime of cot x

e^x

prime of e^x

a^xlna

a^x prime

1/x

ln x prime

(1/ xlna) or (log_ae/x)

(log_ax) prime =2

limits

L’Hospital’s Rule is used to find…