§2.6 Derivatives of inverse functions

Introduction

Basic facts about inverse functions

The derivative of the natural logarithm function

The equation $y = \frac{5}{9}(x-32)$ relates a temperature given in $x$ degrees Fahrenheit to the corresponding temperature $y$ measured in degrees Celsius.

Solve the equation $y = \frac{5}{9}(x-32)$ for $x$ to write $x$ (Fahrenheit temperature) in terms of $y$ (Celsius temperature).

$h(x) = x^2\ln(x)$

$p(t) = \frac{\ln(t)}{e^t + 1}$

$s(y) = \ln(\cos(y) + 2)$

$z(x) = \tan(\ln(x))$

$m(z) = \ln(\ln(z))$