AP Calculus BC – Memorization
CORRECT(Rated A+)
d/dx sin⁻¹x - ANSWER1/√(1-x²) not +/-1
d/dx cos⁻¹x - ANSWER⁻1/√(1−x²) not +/-1
d/dx tan⁻¹x - ANSWER1/(1+x²)
d/dx cot⁻¹x - ANSWER-1/(1+x²)
d/dx sec⁻¹x - ANSWER1/(IxI√(x²-1)) not +/-1,0
d/dx csc⁻¹x - ANSWER-1/(IxI√(x²-1)) not +/-1,0
d/dx sinx - ANSWERcosx
d/dx cosx - ANSWER-sinx
d/dx tanx - ANSWERsec²x
d/dx cscx - ANSWER-cscxcotx
d/dx secx - ANSWERsecxtanx
d/dx cotx - ANSWER-csc²x
∫sinxdx - ANSWER-cosx
∫cosxdx - ANSWERsinx
d/dx e^u - ANSWERe^u(d/dx u)
d/dx a^x - ANSWERa^x(ln(a))
d/dx a^u - ANSWERa^u(ln(a))(d/dx u)
Intermediate Value Theorem - ANSWERf(x) is continuous on [a,b], then the function
takes on every y-value between f(a) and f(b) on the interval (a,b)
Extreme Value Theorem - ANSWERf(x) is continuous on [a,b], f(x) has at least 1
max and 1 min on [a,b]
Mean Value Theorem - ANSWERf(x) is differentiable on (a,b) and thus continuous
[a,b], there is a point c on (a,b) where f'(c)=f(b)-f(a)/b-a, instantaneous rate of
change=average rate of change, slope of tangent line=slope of secant line
