Continuity & differentiability

This chapter teaches about the concepts of differentiability and continuity, composite functions’ derivatives, functions of opposite trigonometric, logarithmic functions and exponentials, statement of mean value and rolle’s formula.

Intermediate 0 Students enrolled
Created by School Prep . Last updated Sat, 10-Apr-2021 English
Curriculum for this course
56 Lessons 45:36:13 Hours
Rational functions differentiation
2 Lessons
  • Differentiating rational functions 00:06:44
  • Quiz 1 3
  • Derivative of e^(cosx)⋅cos(eˣ) 00:05:52
  • Derivative of sin(ln(x²)) 00:04:52
  • Quiz 2 3
  • Derivatives of sin(x), cos(x), tan(x), eˣ & ln(x) 00:03:43
  • Derivative of aˣ (for any positive base a) 00:05:25
  • Worked example: Derivative of 7^(x²-x) using the chain rule 00:03:40
  • Quiz 4 3
  • Derivatives of tan(x) and cot(x) 00:04:38
  • Derivatives of sec(x) and csc(x) 00:04:28
  • Worked example: Derivative of sec(3π/2-x) using the chain rule 00:07:11
  • Quiz 5 3
  • Derivative of logₐx (for any positive base a≠1) 00:04:48
  • Worked example: Derivative of log₄(x²+x) using the chain rule 00:04:10
  • Differentiating logarithmic functions using log properties 00:06:01
  • Quiz 3 3
  • Worked example: Derivative of ∜(x³+4x²+7) using the chain rule 00:05:55
  • Quiz 6 3
  • Continuity introduction 00:11:14
  • Worked example: Continuity at a point (graphical) 00:07:19
  • Quiz 7 3
  • Chain rule 00:05:07
  • Worked example: Derivative of cos³(x) using the chain rule 00:09:17
  • Worked example: Derivative of ln(√x) using the chain rule 00:06:45
  • Worked example: Derivative of √(3x²-x) using the chain rule 00:05:31
  • Worked example: Chain rule with table 00:02:27
  • Quiz 8 3
  • Quotient rule from product & chain rules 00:05:15
  • Worked example: Quotient rule with table 00:05:51
  • Tangent to y= e^x /(2+x³) 00:07:17
  • Normal to y=e^x /x² 00:05:27
  • Quiz 9 3
  • Product rule 00:02:40
  • Differentiating products 00:04:28
  • Worked example: Product rule with table 00:03:09
  • Product rule to find derivative of product of three functions 00:03:34
  • Product rule proof 00:09:26
  • Quiz 10 3
  • Differentiability at a point: graphical 00:05:39
  • Differentiability at a point: algebraic (function is differentiable) 00:05:02
  • Differentiability at a point: algebraic (function isn't differentiable) 00:06:22
  • Quiz 11 3
  • Intermediate value theorem 00:08:05
  • Worked example: using the intermediate value theorem 00:06:43
  • Quiz 12 3
  • Functions continuous on all real numbers 00:03:17
  • Functions continuous at specific x-values 00:04:22
  • Quiz 13 3
  • Limit properties 00:05:08
  • Limits of combined functions 00:04:09
  • Limits of composite functions 00:05:12
  • quiz 14 3
  • Notes
  • Question Bank
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