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If y = f(u) and u = ϕ(x), show that
Solution:
Consider the given two equations above
Since y is a function of u and u is a function of x, then we can apply the derivative of y with respect to x by Chain Rule Method.
Take the derivative of the first equation with respect to u, we have
Take the derivative of the second equation with respect to x, we have
Hence, by Chain Rule Method,
Take the derivative of the above equation with respect to x, we have
but
Hence, the above equation becomes
Therefore,
where
