week 8 Derivative of transcisdental functions

Lecture 1

We find derivatives of trigonometric functions by using following

Lecture 2

Derivatives of Inverse Trigonometric Functions

lecture 3

Derivatives Exponential Functions

In general, an exponential function is of the form

f(x) = ax where a is a positive constant.

Derivative of the Natural Exponential Function

The exponential function f(x) = ex has the property that it is its own derivative. This means that the slope of a tangent line to the curve y = ex at any point is equal to the y-coordinate of the point.

We can combine the above formula with the chain rule to get

Example:

Differentiate the function y = e sin x

Solution:

Example:

Differentiate the function y = e–3xsin4x

Solution:

Using the Product Rule and the above formulas, we get

 

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