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(Steps Shown) Let f:[a, b] \rightarrow R be continuous on [a, b] and let v:[c, d] \rightarrow R be differentiable on $[c, d]$ with v([c, d]) ⊆[a, b].

Question: Let $f:[a, b] \rightarrow \mathbb{R}$ be continuous on [a, b] and let $v:[c, d] \rightarrow \mathbb{R}$ be differentiable on $[c, d]$ with $v([c, d]) \subseteq[a, b]$. If we define $G(x):=\int_{a}^{v(x)} f$, show that $G^{\prime}(x)=f(v(x)) \cdot v^{\prime}(x)$ for all $x \in[c, d]$

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(Steps Shown) Let f:[a, b] \rightarrow R be continuous on [a, b] and let v:[c, d] \rightarrow R be differentiable on $[c, d]$ with v([c, d]) ⊆[a, b].

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