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Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 If you remember your log properties, you can expand or condense first, then take the derivative. 4. ln 1 = 0 2.7 Derivatives of Log Functions

4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

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Page 1: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

If you remember your log properties, you can expand or condense first, then take

the derivative.

4. ln 1 = 0

2.7 Derivatives of Log Functions

Page 2: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Use properties of log to expand:

Page 3: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Now, the Derivatives!

Mem

or

ize t

hese!

*** If you can expand a logarithm first, do it! It makes taking the derivative so much easier!

Page 4: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 5: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

ln (2x4 3x)

Find the derivative.

y =

Page 6: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Find the derivative.

Page 7: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Find the derivatives:

Page 8: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

And this one. . .

Page 9: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Find the slope of the tangent line and the equation of the tangent line at the point (1,0) for

Pg. 318: 15-29 odd, 41-55, 67, 69

Page 10: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 11: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 12: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 13: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 14: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 15: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 16: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 17: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 18: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 19: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 20: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 21: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 22: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Page 23: 4. ln 1 = 0 · 3/3/2017 · Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017 Find the slope of the tangent line and the equation of the tangent line at the point

Day 7 Log Differentiation Notes for 332015.notebook March 03, 2017

Derivatives of Exponential Functions

Mem

or

ize t

hese!

Examples: Solve for the derivative.

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