Exponential Functions – Differentiation and Integration.

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Presentation transcript:

Exponential Functions – Differentiation and Integration

Ex:Solve

Exponential Functions – Differentiation and Integration Ex:Solve

Exponential Functions – Differentiation and Integration

What is the derivative of A natural question to ask is: Remember from the previous section:

Exponential Functions – Differentiation and Integration

AP Calculus BC Tuesday, 26 January 2016 OBJECTIVE TSW differentiate and integrate natural exponential functions. ASSIGNMENTS DUE –WS The Natural Logarithm – Implicit Differentiation and Tangents  wire basket –WS Inverse Functions  black tray TEST: Natural Logarithmic and Natural Exponential Functions – Differentiation and Integration will be this Friday, 29 January QUIZ: Natural Logarithmic Function – Differentiation and Integration will be returned tomorrow. TODAY’S ASSIGNMENT (due on Friday, 01/29/16) –WS Exponential Functions: Differentiation & Integration

Exponential Functions – Differentiation and Integration

Ex:Find the derivative

Exponential Functions – Differentiation and Integration Ex:Find the derivative

Exponential Functions – Differentiation and Integration Ex:Find the POI of

Exponential Functions – Differentiation and Integration Ex:Find the POI of

Exponential Functions – Differentiation and Integration Ex:Find the POI of

Exponential Functions – Differentiation and Integration Ex:Find the POI of

Exponential Functions – Differentiation and Integration Ex:Find the POI of

Exponential Functions – Differentiation and Integration Ex:Find the derivative (implicit differentiation).

Exponential Functions – Differentiation and Integration

Ex:Evaluate Let u = 5x + 3 du = 5 dx 1/5 du = dx

Exponential Functions – Differentiation and Integration Ex:Evaluate Let u = 3x 2 du = 6x dx 1/6 du = x dx

Exponential Functions – Differentiation and Integration Ex:Evaluate Let u = 3/x du = –3/x 2 dx –1/3 du = 1/x 2 dx

Exponential Functions – Differentiation and Integration Ex:Evaluate

Exponential Functions – Differentiation and Integration Ex:Evaluate Let u = 2 + e x du = e x dx

Exponential Functions – Differentiation and Integration Ex:Evaluate Let u = e x du = e x dx