Transcript 5.4 Exponential Functions: Differentiation & Integration

5.4 Exponential Functions:
Differentiation & Integration
• Develop properties of the natural exponential
function.
• Differentiate natural exponential functions.
• Integrate natural exponential functions.
The inverse funciton of the natural logarithmic
function is the natural exponential function.
y=e
if and only if x = ln y
Note: Ln(e ) = x and e = x
Solve 7 = e
ln(2x – 3) = 5
Derivatives of Exponential Function
f(x) = e
f(u) = e
f’(x) = e
f’(u) = e • u’
Integrals of the Exponential Functions
∫ e dx = e + c
∫ e du = e + c