The Natural Logarithmic Function. Differentiation Integration. Properties of the Natural Log Function. If a and b are positive numbers and n is rational, then the following properties are true:. The Algebra of Logarithmic Expressions. The Derivative of the Natural Logarithmic Function.
The Natural Logarithmic Function
Let u be a differentiable function of x
This can get messy with the quotient or product and chain rules. So we will use ln rules to help simplify this and apply implicit differentiation and then we solve for y’…
y= ln|u| as if the absolute value symbol is not even there.
X=-1, Plug back into original to find y
y=ln(1-2+3)=ln2 So, relative extrema is at (-1, ln2)
Let u=4x-1, so du=4dx and dx=
The natural logarithmic function is defined by
The domain of the natural logarithmic function is the set of all positive real numbers
Long Division With Integrals
#1-39, 47-53, 67