See Also
Flashcards
What is the chain rule??
$$ \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx} $$
What new variable do you introduce when using the chain rule??
$$ u $$
When do you apply the chain rule??
When you have composite functions.
$$y = (3x + 4)^5$$ What substitution would you make in order to differentiate??
$$ u = 3x + 4 \\ y = u^5 $$
$$y = u^5$$ What is $\frac{dy}{du}$??
$$ 5u^4 $$
$$u = 3x -1$$ What is $\frac{du}{dx}$??
$$ 3 $$
$$y = (3x + 4)^5 \ u = 3x + 4 \ y = u^5 \ \frac{dy}{du} = 5u^4 \ \frac{du}{dx} = 3$$ What is $\frac{dy}{dx}$??
$$ 15(3x + 4)^4 $$
$$\ln \boxed{beans}$$ How much does the $\ln$ bit “wiggle”??
$$ \frac{1}{\boxed{beans}} $$
$$\ln \boxed{beans}$$ What’s the derivative??
$$ \frac{1}{\boxed{beans}} \times (\frac{dy}{d(beans)} \boxed{beans}) $$
What’s an analogy for the chain rule??
Multiplying how much stuff wiggles.
$$\ln (2x + 5)$$ What’s the derivative??
$$ \frac{2}{2x + 5} $$
$$(3x-1)^4$$ What’s the derivative??
$$ 12(3x-1)^3 $$
$$(2x + 3)^5$$ What’s the derivative??
$$ 10(2x + 3)^4 $$
$$(x + 7)^9$$ What’s the derivative??
$$ 9(x + 7)^8 $$
$$\ln \boxed{2x}$$ How much “wiggle” does the $2x$ contribute??
$$ 2 $$
Backlinks
- [[Maths - Quotient Rule]]S
- [[Maths - Differentiation]]S
- [[Maths - Product Rule]]S
- [[Maths - Syllabus]]S
Metadata
date: 2021-02-03 14:35
tags:
- '@?maths'
- '@?further-maths'
- '@?public'
- '@?differentiation'
title: Maths - Chain Rule