EE-Learning
Showing explicit and implicit differentiation give same result
Catogry:
Math
Subject:
AP Calculus BC
Course:
Differentiation: Composite, Implicit, And Inverse Functions
Lecture List
Quotient rule from product & chain rules
Chain rule proof
If function u is continuous at x, then Δu→0 as Δx→0
Proof: Differentiability implies continuity
Disguised derivatives
Second derivatives (implicit equations): evaluate derivative
Second derivatives (implicit equations): find expression
Second derivatives
Derivative of sin(ln(x²))
Derivative of eᶜᵒˢˣ⋅cos(eˣ)
Applying the chain rule twice
Applying the chain rule and product rule
Differentiating using multiple rules: strategy
Manipulating functions before differentiation
Differentiating functions: Find the error
Derivative of inverse tangent
Derivative of inverse cosine
Derivative of inverse sine
Derivatives of inverse functions: from table
Derivatives of inverse functions: from equation
Derivatives of inverse functions
Showing explicit and implicit differentiation give same result
Worked example: Evaluating derivative with implicit differentiation
Worked example: Implicit differentiation
Implicit differentiation
Worked example: Derivative of ∜(x³+4x²+7) using the chain rule
Worked example: Derivative of sec(3π/2-x) using the chain rule
Worked example: Derivative of log₄(x²+x) using the chain rule
Worked example: Derivative of 7^(x²-x) using the chain rule
Derivative of logₐx (for any positive base a≠1)
Derivative of aˣ (for any positive base a)
Worked example: Chain rule with table
Worked example: Derivative of ln(√x) using the chain rule
Worked example: Derivative of √(3x²-x) using the chain rule
Worked example: Derivative of cos³(x) using the chain rule
Identifying composite functions
Common chain rule misunderstandings
Chain rule