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$\begingroup$ @Doc : Any rule about how to apply an operation to a composite of functions may be called a chain rule. The chain rule for differentiation is most famous, but there's also a chain rule for limits. (Similarly for product rules, sum rules, etc.) $\endgroup$ –
17 Αυγ 2024 · Instead, we use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
7 Ιουν 2024 · The chain rule formula is used to differentiate a composite function such as (ln x) 2, (x 2 + 1) 3 and others, whereas the product rule is used to find the derivative of the product of two functions, such as sin x · ln x, x 2.ln x, and others.
15 Φεβ 2021 · The Chain Rule formula shows us that we must first take the derivative of the outer function keeping the inside function untouched. Essentially, we have to melt away the candy shell to expose the chocolaty goodness. Then we multiply by the derivative of the inside function.
16 Νοε 2022 · In this section we discuss one of the more useful and important differentiation formulas, The Chain Rule. With the chain rule in hand we will be able to differentiate a much wider variety of functions.
For example, to find derivatives of functions of the form \(h(x)=\left(g(x)\right)^n\), we need to use the Chain Rule combined with the Power Rule. To do so, we can think of \(h(x)=\left(g(x)\right)^n\) as \(f\left(g(x)\right)\) where \(f(x)=x^n\).
We can directly use the limit definition, or in some cases we have rules to compute them, such as the power rule; if our function is formed as a sum, difference, product, or quotient of two functions whose derivatives we know, we can compute the derivative using linearity or the product or quotient rules.
