# Differentiation of Transcendental Functions

## In this Chapter

### a. Differentiating Trigonometric Functions

- 1. Derivatives of Sin, Cos and Tan Functions
- 2. Derivatives of Csc, Sec and Cot Functions
- 3. Derivatives of Inverse Trigonometric Functions (like `arcsin x`, `arctan x`, etc)
- 4. Applications: Derivatives of Trigonometric Functions (rate of change, engineering, equation of normal)

### b. Differentiating Logarithmic and Exponential Functions

- 5. Derivative of the Logarithmic Function
- 6. Derivative of the Exponential Function (like
*e*^{x}) - 7. Applications: Derivatives of Logarithmic and Exponential Functions (sound intensity - decibels, aviation, electronics, radius of curvature, maximisation)

### Related Sections in "Interactive Mathematics"

The Derivative, an introduction to differentiation, (for the newbies).

Integration, which is actually the opposite of differentiation.

Differential Equations, which are a different type of integration problem that involve differentiation as well.

See also the Introduction to Calculus, where there is a brief history of calculus.

### Some definitions

**transcendental** *adj.* abstract; obscure; visionary

**transcendental function** *n.* a non-algebraic function.

Examples: `sin(x)`; `log(x)`; `arccos(x)`

## Why study this...?

There are many technical and scientific applications
of exponential (*e*^{x}), logarithmic (`log x`) and trigonometric functions (`sin x`, `cos x`, etc).

In this chapter, we find
formulas for the derivatives of such transcendental functions. We need to
know the **rate of change** of the functions.

Rafiki, meditating on things transcendental...

We begin with the formulas for Derivatives of sine, cosine and tangent »