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AP Calculus

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d/dx(e^x)

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Calculus Math

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Mar 1, 2020

Cards (37)

Section 1

(37 cards)

d/dx(e^x)

Front

e^x

Back

Product Rule

Front

d/dx = u'v + uv'

Back

d/dx(tan x)

Front

[sec x]^2

Back

d/dx(cos^-1(x))

Front

-1/sqrt(1-x^2)

Back

d/dx(csc^-1(x))

Front

-1/|x|sqrt(x^2-1)

Back

Calculus solves these 2 kinds of problems

Front

analyse rates of change of functions & calculate areas under the curve

Back

where f(x) decreases

Front

f'(x) is negative

Back

intermediate value theorem

Front

If f is continuous on [a,b] and y is a number between f(a) and f(b), then there exists at least one number c such that f(c)=y

Back

slope of a secant line

Front

average rate of change

Back

d/dx(cot x)

Front

-(csc x)^2

Back

point-slope form

Front

y-y1=m(x-x1)

Back

f(x)=h(g(x)), f'(x)=

Front

h'(g(x)) * g'(x)

Back

where f(x) increases

Front

f'(x) is positive

Back

d/dx(cot^-1(x))

Front

-1/(x^2+1)

Back

3 types of discontinuity

Front

step discontinuity, removable discontinuity, and infinite discontinuity

Back

d/dx(csc x)

Front

-csc x cot x

Back

d/dx(sin x)

Front

cos x

Back

d/dx(sec x)

Front

sec x tan x

Back

4 basic concepts

Front

limit, derivative, integral, integral

Back

d/dx(b^x)

Front

b^x * ln b

Back

slope of a tangent line

Front

instantaneous rate of change

Back

d/dx(lnx)

Front

1/x

Back

average rate of change

Front

f(b)-f(a)/b-a or f(x)-f(c)/x-c

Back

instantaneous rate of change

Front

lim b->a (f(b)-f(a)/b-a) or lim x->c (f(x)-f(c)/x-c)

Back

h form

Front

lim h->0 f(x+h)-f(x)/h

Back

sinusoidal function general form

Front

f(x)=C+Asin[B(x-D)]

Back

area under the curve

Front

definite integral

Back

0/0

Front

indeterminate

Back

where f(x) has a local max/min

Front

then f'(x) will have a zero

Back

limit

Front

the y-value the graph approaches as the x-value approaches a certain number

Back

d/dx(cos x)

Front

-sin x

Back

d/dx(sin^-1(x))

Front

1/sqrt(1-x^2)

Back

Quotient Rule

Front

d/dx = (u'v-uv')/v²

Back

4 representations of calculus

Front

algebraic, graphically, numerical, verbal

Back

d/dx(tan^-1(x))

Front

1/(x^2+1)

Back

17/0

Front

undefined

Back

d/dx(sec^-1(x))

Front

1/|x|sqrt(x^2-1)

Back