Chain/Exponential/Log Derivatives Review

\sin(x)

\cos(x)

\cos(x)

-\sin(x)

\tan(x)

\sec^2(x)

\cot(x)

-\csc^2(x)

\sec(x)

\sec(x)\tan(x)

\csc(x)

-\csc(x)\cot(x)

x^n

nx^{n-1}

f \cdot g

f' \cdot g + g' \cdot f

f/g

(g \cdot f' - f \cdot g')/(g^2)

f(g(x))

(f' \cdot g(x)) \cdot g'

e^x

e^x

a^x

a^x \cdot \ln(a) \cdot x'

\log_a u

u'/(u \cdot \ln(a))

\ln(u)

u'/u