chain rule formula

chain rule formula The chain rule combines with the power rule to form a new rule If h x big g x big n then h x n big g x big n 1 cdot g x When applied to the composition of three functions the chain rule can be expressed as follows If h x f Big g big k x big Big then h x f Big g big k x big Big cdot

The chain rule says d d x f g x f g x g x It tells us how to differentiate composite functions Quick review of composite functions A function is composite if you can write it as f g x In other words it is a function within a function or a function of a function For example cos The Chain Rule Formula is as follows LARGE frac dy dx frac dy du frac du dx Solved Examples on Chain Rule Formula Example 1 Differentiate y cos x2 Solution Given y cos x2 Let u x2 so that y cos u Therefore begin array l frac du dx 2x end array

chain rule formula

chain rule formula
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The Chain Rule tells us how Example Sage the Dog can run 3 times faster than you and you can run 2 times faster than me so Sage can run 3 2 6 times faster than me Let s use some notation Call the dog y me x and you can be u dy dx is Sage s speed relative to me dy du is Sage s speed relative to you There are two forms of chain rule formula as shown below Chain Rule Formula 1 d dx f g x f g x g x Example To find the derivative of d dx sin 2x express sin 2x f g x where f x sin x and g x 2x Then by the chain rule formula d dx sin 2x cos 2x 2 2 cos 2x Chain Rule Formula 2

Chain Rule Suppose that we have two functions f x f x and g x g x and they are both differentiable If we define F x f g x F x f g x then the derivative of F x F x is F x f g x g x F x f g x g x What is the Chain Rule The chain rule is used to calculate the derivative of a composite function The chain rule formula states that dy dx dy du du dx In words differentiate the outer function while keeping the inner function the same then multiply this by the derivative of the inner function The Chain Rule Leibniz Notation

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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 x is a composite function because it can be constructed as f g x for f x sin x and g x x 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 To put this rule into context let s take a look at an example h x sin x 3

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chain rule formula - There are two forms of chain rule formula as shown below Chain Rule Formula 1 d dx f g x f g x g x Example To find the derivative of d dx sin 2x express sin 2x f g x where f x sin x and g x 2x Then by the chain rule formula d dx sin 2x cos 2x 2 2 cos 2x Chain Rule Formula 2