AP Calc AB 3.4

Inverses

Exponents and logarithms are _____ of each other.

Negative

You can't have a ____ log.

1/xlna

Derivative of loga(x)

1/x

Derivative of lnx

u'(x)/u(x)

Derivative ln[u(x)]. This is if there is a function within a natural log. A function must change the input.

1/x

Derivative of ln|x|

Logarithmic Differentiation

When you natural log both sides of an equation. This is where you enact the properties of exponents and logarithms.

1/y (dy/dx)

What is lny? When you take 1/y to the other side yo will have to multiply by y, which is your original equation.

ax^a-1

Derivative of x^a. It's just like the power rule.

x

Simplify e^lnx.