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AP Calculus AB - Derivatives

AP Calculus AB - Derivatives

memorize.aimemorize.ai (lvl 286)
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23 cards
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Section 1

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Mean Value Theorem

Front

1 / 23

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Last updated

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Mar 1, 2020

Cards (23)

Section 1

(23 cards)

Mean Value Theorem

Front

f'(c) = (f(b) - f(a))/ (b - a)

Back

Derivative of arccos(x)

Front

-du/sqrt(1-u^2)

Back

Derivative of sec(x)

Front

secutanu du

Back

Derivative of ln(x)

Front

du/u

Back

Derivative of cos(x)

Front

-sinu du

Back

Derivative of sin(x)

Front

cosu du

Back

Derivative of csc(x)

Front

-cscucotu du

Back

Quotient Rule

Front

Bot dervTop - top dervBtm/btm^2

Back

Vertical Tangents

Front

Set denominator of Derivative equal to 0

Back

Derivative of arctan(x)

Front

du/(1+u^2)

Back

Derivative of tan(x)

Front

sec^2u du

Back

Derivative of arcsec(x)

Front

du/abs(u)sqrt(u^2-1)

Back

Derivative of a^x

Front

(a^u) ln(a) du

Back

Derivative of e^x

Front

e^u du

Back

Derivative of cot(x)

Front

-csc^2u du

Back

Derivative of log(x) -- (base of a)

Front

du/(u ln(a) )

Back

Find the rate of change, in km/hr, of the distance between the two ships when x = 4 km and y = 3 km

Front

1. r^2=x^2+y^2 2. 2rdr/dt=2xdx/dt+2ydy/dt 3. 2rdr/dt=2xdx/dt+2ydy/dt Defined at know points 4. dr/dt=4(-15) + 3(10)/5 5. All equals -6km/hr

Back

Derivative of arccot(x)

Front

-du/(1+u^2)

Back

Horizontal Tangents

Front

Set numerator of derivative equal to 0

Back

Outside Inside(F(g(x)))

Front

F'(g(x)) g'(x)

Back

Derivative of arccsc(x)

Front

-du/abs(u)sqrt(u^2-1)

Back

Product Rule

Front

1st derv2nd + 2nd derv1st

Back

Derivative of arcsin(x)

Front

du/sqrt(1-u^2)

Back