What is Chain rule?
In [[differential calculus]], the '''chain rule''' is a way of finding the [[derivative (mathematics)|derivative]] of a [[function (mathematics)|function]]. It is used where the function is within another function. This is called a [[Function composition|composite function]]. More specifically, if <math>F(x)</math> equals the composite function of the form: :<math>F(x)=f(g(x))</math> where ''g'' is a function differentiable at ''x'' and ''f'' is a function differentiable at ''g''(''x''), then the derivative of <math>F(x)</math>, written as <math>F'(x)</math>, exists, and is equal to :<math>F'(x)=f'(g(x))g'(x)</math>.<ref>{{Cite web|date=2016-06-05|title=Chain Rule for Derivative — The Theory|url=https://mathvault.ca/chain-rule-derivative/|access-date=2020-09-19|website=Math Vault|language=en-US}}</ref><ref>{{Cite web|title=Chain rule (article)|url=https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/a/chain-rule-review|access-date=2020-09-19|website=Khan Academy|language=en}}</ref><ref>{{Cite web|last=Kouba|first=Duane|date=May 6, 1997|title=Differentiation Using the Chain Rule|url=https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html|archive-url=|archive-date=|access-date=September 19, 2020|website=math.ucdavis.edu}}</ref> ==Steps== '''1.''' Find the derivative of the outside function (all of it at once). '''2.''' Find the derivative of the inside function (the bit between the [[Bracket|brackets]]). '''3.''' [[Multiply]] the answer from the first step by the answer from the second step. This is basically the last step in solving for the derivative of a function. For example, :<math>F(x) = (x^2+5)^3 
ightarrow 3(x^2+5)^2</math> :<math>F'(x)=3(x^2+5)^2(2x) =6x(x^2+5)^2</math> In this example, the cubed sign (<sup>3</sup>) is the outside function and <math>x^2+5</math> is the inside function. The derivative of the outside function would be <math>3x^2</math>, where ''x'' is replaced by the inside function. The derivative of the inside function wo