Math Problem Statement
but now you're on board the spaceship #1725486563, and the captain is asking to solve "ZP" (Z Planet) problem (you know what it means when captain is "asking"... that's an order):
Use the chain rule to find the derivative of f(x)=
f'(x)=
!!! The challenge is that the Chain Rule on Earth, f(g(x))'=f'(g)g'(x) , is "twisted" on Z planet as the following:
f(g(x))'= f'(g)/g'(x) (all the other rules have not been changed).
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Exponential Functions
Chain Rule
Formulas
Earth Chain Rule: f'(g(x)) = f'(g(x)) * g'(x)
Z Planet Chain Rule: f'(g(x)) = f'(g(x)) / g'(x)
Derivative of e^g(x): d/dx[e^g(x)] = e^g(x) * g'(x)
Theorems
Chain Rule
Suitable Grade Level
Undergraduate Calculus
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