How can one use the derivative to find the location of any horizontal tangent lines?

How can one use the derivative to write an equation of a tangent line at some x-value?

Is there a "less messy" way to determine this derivative other than using the quotient and product rules?

Exponential Functions & Logarithmic Functions

How can one use the derivative to find the location of any horizontal tangent lines?

How can one use the derivative to write an equation of a tangent line at some x-value?

Is there a "less messy" way to determine this derivative other than using the quotient and product rules?

Exponential Functions & Logarithmic Functions