Derivatives of Polynomials and Exponential Functions

1
Derivatives of Polynomials and Exponential
Functions
Derivative of a constant function
2
Derivatives of Polynomials and Exponential
Functions
Power Functions
The Power Rule
3
Derivatives of Polynomials and Exponential
Functions
The Constant Multiple Rule
4
Derivatives of Polynomials and Exponential
Functions
The Sum Rule
The Difference Rule
5
Derivatives of Polynomials and Exponential
Functions
Find an equation of the tangent to the curve
given
6
Derivatives of Polynomials and Exponential
Functions
Exponential Functions
7
Derivatives of Polynomials and Exponential
Functions
This shows that the exponential. function is
differentiable at 0, therefore it is
differentiable everywhere
This shows that the rate of change of any
exponential. function is proportional to the
function itself.
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Derivatives of Polynomials and Exponential
Functions
Definition of e
Derivative of the Natural Exponential Function
9
Derivatives of Polynomials and Exponential
Functions
10
Derivatives of Polynomials and Exponential
Functions
Compare the graphs of f (x) and f(x).
Use the following windows x-10, 10, y -2, 2
11
Derivatives of Polynomials and Exponential
Functions
Find the equation of a tangent line to the curve
at the given point.