Math. 69.107GH

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1. Let f, g be differentiable functions with f'(0)=1, g(-1)=0 and g'(-1)=2. Assume that the range of g is contained in the domain of f. What is the value of the derivative of the composition fog at x=-1? Hint:Use the Chain Rule...

2

0

-1

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2. Let F be in the inverse function of f. Using the chain rule it can be shown that F'(x) = 1/f'(F(x)), i.e., the reciprocal of f'(F(x)).Given that F(0)=2 and f'(2) = -1 what is the value of F'(0)?

1

-1

0

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3. What is the derivative of the function f(x) = sqrt(x) sec (sqrt(x)) ?

sec (sqrt(x)) tan (sqrt(x) / 2sqrt(x)

sec (sqrt(x)) / 2 sqrt(x)

sec (sqrt(x)) [sqrt(x) tan (sqrt(x)) + 1] / 2 sqrt(x)

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