AP Calc Unit 1-4 Review

d/dx sin⁻¹(x)

1/√(1-x²)

d/dx cos⁻¹(x)

-1/√(1-x²)

d/dx tan⁻¹(x)

1/(1+x²)

d/dx csc⁻¹(x)

-1/(|x| √(x²-1))

d/dx sec⁻¹(x)

1/(|x| √(x²-1))

d/dx cot⁻¹(x)

-1/(1+x²)

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec² (x)

d/dx csc (x)

-csc(x)cot(x)

d/dx sec(x)

sec(x)tan(x)

d/dx cot(x)

-csc²(x)

d/dx a^x

a^x * lna

d/dx logAx

1/x * ln(a)

d/dx lnx

1/x

L’Hopital’s rule

lim x—>a f(x)/g(x) = lim x—> f’(x)/g’(x)

When f is increasing, f’ is

positive

When f is decreasing, f’ is

negative

When f has an extrema

f’ = 0 and sign change

When f is concave up f’ is ? f’’ is?

f’ is increasing, f’’ is positive

When f is concave down, f’ is? f’’ is?

f’ is decreasing, f’’ is negative

When f has a point of inflection

f’ has an extrema, f’’ = 0 and sign change

d/dx of g(x) = inverse of f(x)

g’(x) = 1/f’(g(x))