Advanced differentiation

The chain rule sets the stage for implicit differentiation, which in turn allows us to differentiate inverse functions (and specifically the inverse trigonometric functions). This is really the top of the line when it comes to differentiation.

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Created by School Prep . Last updated Fri, 16-Apr-2021 English
Curriculum for this course
34 Lessons 34:26:42 Hours
Implicit differentiation introduction
5 Lessons
  • Implicit differentiation 00:08:02
  • Worked example: Implicit differentiation 00:04:55
  • Worked example: Evaluating derivative with implicit differentiation 00:05:25
  • Showing explicit and implicit differentiation give same result 00:07:48
  • Quiz 1 5
  • Implicit differentiation (advanced example) 00:04:08
  • Implicit differentiation (advanced example) 00:07:10
  • Implicit differentiation (advanced example) 00:05:58
  • Derivative of ln(x) from derivative of 00:03:08
  • Quiz 2 5
  • Derivative of inverse sine 00:04:56
  • Derivative of inverse cosine 00:03:44
  • Derivative of inverse tangent 00:06:02
  • Quiz 3 5
  • Derivatives of inverse functions: from equation 00:05:04
  • Derivatives of inverse functions: from table 00:05:12
  • Quiz 4 5
  • Proof: d/dx(ln x) = 1/x 00:09:52
  • Proof: d/dx(eˣ) = eˣ 00:04:40
  • Proofs of derivatives of ln(x) and eˣ 00:12:27
  • Quiz 5 5
  • Composite exponential function differentiation 00:09:02
  • Worked example: Composite exponential function differentiation 00:08:44
  • Quiz 6 5
  • Second derivatives 00:02:27
  • Quiz 7 1
  • Mean value theorem 00:06:37
  • Mean value theorem example: polynomial 00:07:45
  • Mean value theorem example: square root function 00:06:24
  • Mean value theorem application 00:07:12
  • quiz 8 1
  • Notes
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