What does it mean by "we differentiate the outer function f [at the inner function g(x)]" portion of the Chain Rule?

Question

anonymous · Answer

multiply by the exponent of the fn then minus one on the exponent ,that must be multiplied by the inner function

anonymous · Answer

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anonymous · Answer

Say you have a function $$(2x+1)^2$$ The outer function is $$f(x) = x^2$$ And the inner function is $$g(x) = 2x + 1$$.. The chain rule says if you have $$y = f(g(x))$$ then to find the derivative you do $$f \prime(g(x)) * g \prime (x)$$ You find the derivative of the outer function (f(x)) and keep the inner function (g(x)) the same then multiply it by the derivative of the inner function (g(x)). Hope this helps.

anonymous · Answer

So the derivative of $$(2x + 1)^2$$ Would be $$2(2x+1) * 2$$ Which is 8x + 4

anonymous · Answer

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