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I am struggling with this question:

Suppose u and v are functions of x that are differentiable at x=0 and that u(0)=2, u'(0)=10, v(0)=-4 and v'(0)=-5

If f(x)=u/v, find f'(0)

Sorry about taking that many days, but I just got to making a response.

It is known by the quotient rule that f'(x) = (vu' - uv')/v^2.

The values for u, u', v, and v' are given as 2, 10, -4, and -5 respectively.

That gives f'(0) = (-4*10 - 2*[-5])/(-4)^2.

That gives f'(0) = (-40 + 10)/16 = -30/16 = -15/8 = -1 7/8 = -1.875.

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