Formulae and Theorems
Survey of Calculus M161
Midterm 2
Formulae and Theorems
Exponential and Logarithmic Function d (ex) = ex dx
d
1
ln(x) =
dx
x
The Product Rule d (f (x)g(x)) = f (x)g0(x) + f 0(x)g(x) dx
The Quotient Rule d f (x)
g(x)f 0(x) f (x)g0(x)
= dx g(x)
g(x)2
The Chain Rule
d f (u(x)) = f 0(u(x)) du
dx
dx
The Chain Rule using the power rule
d u(x)n = nu(x)n 1 du
dx
dx
The Chain Rule with Exponential Functions
d eu(x) = eu(x) du
dx
dx
The Chain Rule with Logarithmic Functions
d
1 du
ln(u(x)) =
dx
u(x) dx
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