CALC AB CHAPTER FOUR TUFF DERIVATIVES I HATE PRETTY ASIAN LADIES

d/dx(sin x)

cos x

d/dx(cos x)

-sin x

d/dx(tan x)

sec^2 x

d/dx(cot x)

-csc^2 x

d/dx(sec x)

sec x * tan x

d/dx(csc x)

-csc x * cot x

d/dx(sin u)

cos u * u'

d/dx(cos u)

-sin u * u'

d/dx(tan u)

sec^2 u * u'

d/dx(cot u)

-csc^2 u * u'

d/dx(sec u)

sec u * tan u * u'

d/dx(csc u)

-csc u * cot u * u'

d/dx(arcsin x)

1 / sqrt(1 - x^2)

d/dx(arccos x)

-1 / sqrt(1 - x^2)

d/dx(arctan x)

1 / (1 + x^2)

d/dx(arccot x)

-1 / (1 + x^2)

d/dx(arcsec x)

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

d/dx(arccsc x)

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

d/dx(arcsin u)

(1 / sqrt(1 - u^2)) * u'

d/dx(arccos u)

(-1 / sqrt(1 - u^2)) * u'

d/dx(arctan u)

(1 / (1 + u^2)) * u'

d/dx(arccot u)

(-1 / (1 + u^2)) * u'

d/dx(arcsec u)

(1 / (|u| * sqrt(u^2 - 1))) * u'

d/dx(arccsc u)

(-1 / (|u| * sqrt(u^2 - 1))) * u'

d/dx(e^x)

e^x

d/dx(a^x)

a^x * ln(a)

d/dx(ln x)

1 / x

d/dx(log_a x)

1 / (x * ln(a))

d/dx(e^u)

e^u * u'

d/dx(a^u)

a^u * ln(a) * u'

d/dx(ln u)

(1 / u) * u'

d/dx(log_a u)

(1 / (u * ln(a))) * u'

If f(a) = b and f'(a) = m

then (f^-1)'(b) = 1 / m