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 ex)
- 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.
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 (ex), 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 »