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BifSlamkovich
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Homework Statement
First problem:
Data in the form of a table is given for all integers x in [-2,3], f(x), g(x), f'(x), and g'(x)
Given that h(x) = g(2/x), find h'(2/3)
Second problem:
Given g(x) = ∫2-3xx2 f(t) dt, and h(x) = g(x2), find the derivative of h'(x)? Lower bound on the integral is 2-3x and upper bound is x2.
Homework Equations
The Attempt at a Solution
First problem:
Do we or do we not apply the chain rule? Since h(x) = g(2/x), then does h'(x) = g'(2/x)?
Second problem:
We can simplify g(x) to the integral f(t) evaluated at x2 - the integral of f(t) evaluated at 2-3x. If g(x) is equal to this, then the derivative of it is 2x*f(x2) - 3*f(2-3x), since where taking derivative wrt x. Then finally, we plug in x2 wherever there is an x to get h'(x) (=g'(x2)