Let g : R → R be differentiable at a point xo and define f : R → R by f (x) = xg(x). Using the definition of the derivative, prove that f is differen- tiable at ro and that f'(xo) = xog'(xo)+ g(xo). (NB: You are not allowed to use any Rules of Differentiation, such as the Prod- uct Rule. You are allowed to use Limit Rules from Chapter 3 in Notes/Ross.)

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A: NOTE: Refresh your page if you can't see any equations. . take derivative divide both sides by…

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A: Given :                f(x) = x Definition :                      f'(x) = limh→0 f(x+h)-f(x)h

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Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

Q: y/= (x- sin(x2-7) + In(5x-x³+1))/

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