- #1
meredith
- 16
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Homework Statement
f(x) = e^(2x) and g(x) = lnx. what is the derivative of f(g(x)) at x=e
Homework Equations
dy/dx = f'g(x) x g'(x)
The Attempt at a Solution
i can't figure it out!
The derivative of f(x) = e^(2x) is f'(x) = 2e^(2x).
The derivative of g(x) = lnx is g'(x) = 1/x.
The composite function f(g(x)) is e^(2lnx).
The derivative of f(g(x)) at x=e is f'(g(e)) * g'(e) = (2e^(2lnx))|x=e * (1/x)|x=e = 2e^2.
The chain rule can be applied by first finding the derivative of f(g(x)) and then substituting x=e into both f'(g(e)) and g'(e).