Use Calculus I tools and the Componentwise Differentiation Theorem from class to prove the Chain Rule...

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Use Calculus I tools and the Componentwise Differentiation Theorem from class to prove the Chain Rule for vector functions. That is, if ~u : R→ R^n and f: R→ Rare differentiable at f(t) and t respectively, prove d/dt(u(f(t))) = f'(t)u'(f(t)). This problem is asking you to prove differentiation property 6 from the book, so you cannot cite that property as part of your proof! Use only Calculus I knowledge, the Componentwise Differentiation Theorem, and algebraic vector operations. As usual, work LHS to RHS or vice versa, justify each step in words using appropriate terminology, and do not combine operations or theorems. Use Calculus I tools and the Componentwise Differentiation Theorem from class to prove the Chain Rule for vector functions. That is, if ~u : R→ R^n and f: R→ Rare differentiable at f(t) and t respectively, prove d/dt(u(f(t))) = f'(t)u'(f(t)). This problem is asking you to prove differentiation property 6 from the book, so you cannot cite that property as part of your proof! Use only Calculus I knowledge, the Componentwise Differentiation Theorem, and algebraic vector operations. As usual, work LHS to RHS or vice versa, justify each step in words using appropriate terminology, and do not combine operations or theorems.

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