fa.functional analysis - Taylor serie on a Riemannian manifold

Prove that $operatorname{grad}(f(u(x_1, …, x_m), v(x_1, …, x_m))) = frac{df}{du} operatorname{grad}u + frac{df}{dv} operatorname{grad}dv$ Answer

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Prove that $operatorname{grad}(f(u(x_1, …, x_m), v(x_1, …, x_m))) = frac{df}{du} operatorname{grad}u + frac{df}{dv} operatorname{grad}dv$

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$operatorname{grad}(f(u(x_1, …, x_m), v(x_1, …, x_m))) = frac{partial f}{partial u} operatorname{grad}u + frac{partial f}{partial v} operatorname{grad} v$

I don`t know the way to show that, ameliorate pls:(

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