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Unit 7: Product, quotient, & chain rules.
Multivariable chain rule intro. Multivariable chain rule intuition. Multivariable chain rule. Vector form of the multivariable chain rule. Multivariable chain rule and directional derivatives. More formal treatment of multivariable chain rule.
Learn how to apply the chain rule twice in calculus with Khan Academy's video tutorial.
Derivatives of vector-valued functions. Curvature. Multivariable chain rule, simple version. Partial derivatives of parametric surfaces.
What is the "reverse chain rule", and why it does the same thing as u-substitution.
Course: AP®︎/College Calculus AB > Unit 6. Lesson 11: Integrating using substitution. 𝘶-substitution intro. 𝘶-substitution: multiplying by a constant.
We explore the connection between the quotient rule, product rule, and chain rule in calculus. Rather than memorizing another rule, we see how the quotient rule naturally emerges from applying the product and chain rules.
Let's explore a worked example of differentiating the logarithmic function log₄ (x²+x) using the chain rule. Leveraging our understanding of the derivative of logₐ (x), we simplify the complexities of composite functions, making differentiation more approachable and fun!
The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².