University⏱ 4 min

Chain Rule

Derivative of composite function

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slope=0.969
x = 0.50
\ racddxf(g(x))=f′(g(x))⋅g′(x)\ rac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x)
ddx[sin⁡(x2)]=cos⁡(x2)⋅2x\frac{d}{dx}[\sin(x^2)] = \cos(x^2) \cdot 2x

Chain rule: derivative of a composite function = outer derivative × inner derivative. "Differentiate the outside, keep the inside, multiply by the derivative of the inside."