There is the relationship between the dierivative of a function and the derivative of its inverse.  You will explore this as part of today's lesson.

You will also begin looking at inverse of trigonometric functions.  In order to make the inverse a function, we need to restrict the domain of the trigonometric function.

Resources

  • Notes

Assignment

  • p162 #20
  • p162 #1-5, 7, 10
Attachments:
FileDescriptionFile size
Download this file (3.1.notes.pdf)3.1.notes.pdf 4025 kB

Resources

  • Notes

Assignment

  • Worksheet from notes booklet (note the answer for #6 should be
  • p48 #7-10, 31, 32
Attachments:
FileDescriptionFile size
Download this file (3.2.notes.pdf)3.2.notes.pdf 398 kB

Inverse trigonometric functions can be differentiated using implicit differentiation!  Today we will determine general forms for the derivatives of inverse trigonometric functions.

Resources

  • Notes

Assignment

  • p162 #1-5
Attachments:
FileDescriptionFile size
Download this file (3.3.notes.v2016.pdf)3.3.notes.v2016.pdf 471 kB

Derivatives of exponential functions are based on the exponential function.  The derivative is pretty basic, and you should be able to follow the proof, but will not need to know it for your test.

Assignment: p170 #1-17, 41, 47, 49

Attachments:
FileDescriptionFile size
Download this file (3.5a.notes.pdf)3.5a.notes.pdf 118 kB
Download this file (3.5b.notes.pdf)3.5b.notes.pdf 230 kB

Today, we will find the derivative of y = ln x using the fact that it is the inverse of the function y = e^x.  There are a couple of different ways to determine this, and we will make use of the properties of logarithms to differentiate more complicated logarithmic functions as well.

Assignment p170 #19-39

Attachments:
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Download this file (3.6.notes.pdf)3.6.notes.pdf 419 kB

Some functions could be very complicated when we try to differentiate them, as they may be a mix of several product rule, quotient rule and chain rule problems strung together.  One way to simplify the problem is using the properties of logarithms.

Recall that for y = ln (ab) can be rewritten as y= lna + lnb and that y=ln(a/b) can be rewritten as y= lna - lnb

 

Assignment p170 #43-46, 48, 52, 53

Attachments:
FileDescriptionFile size
Download this file (3.7.notes.pdf)3.7.notes.pdf 655 kB
   
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