If h(x) = f(g(x)), what is h'(x)? (Chain rule)
f'(g(x)) * g'(x)
To find the derivative of h(x), we need to use the chain rule of differentiation, which states that if y = f(u) and u = g(x), then the derivative of y with respect to x can be written as:
dy/dx = dy/du * du/dx
Applying this rule to the function h(x) = f(g(x)), we have:
h'(x) = d/dx[f(g(x))] = f'(g(x)) * g'(x)
So, h'(x) is equal to the product of the derivative of the outer function f evaluated at the inner function g(x) and the derivative of the inner function g(x) with respect to x.
In summary, the derivative of h(x) = f(g(x)) with respect to x is h'(x) = f'(g(x)) * g'(x).
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