What is the chain rule?
A special rule, the chain rule, exists for differentiating a function of another function (finding dy/dx).
Consider the expression cos x2 . We call such an expression a ‘function of a function’. We could identify them more mathematically by saying that f(x) = cos x and g(x) = x2, such that f(g(x)) = f(x2) = cos x2.
How to use the chain rule:
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substitute u = g(x), which gives y = f(u)
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Use the chain rule: dy/dx= dy/du × du7dx.
Example: differentiate y = cos x2
Let u = x2 and y = cos u
du/dx = 2x and dy/du = -sin u.
Use the chain rule: dy/dx = dy/du × du/dx = -sin u × 2x = -2x sin x2
DM
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