Differentiation of Transcendental Functions

transcendental adj. abstract; obscure; visionary

transcendental function n. a non-algebraic function.
Examples: sine(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). (See some of the uses of trigonometry.)

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

In this Chapter

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)

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)

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