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Differentiable functions of x

  • Thread starter carlarae
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  • #1
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Homework Statement


Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative.
u(1)=2, u'(1)=-7, v(1)=7,v'(1)=-2
d/dx (uv) at x =1


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gb7nash
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What have you tried?
 
  • #3
Simon Bridge
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Hint

Homework Equations


look for the equations you use when you have to differentiate a combination of two functions... one of them looks like your problem.
 
  • #4
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I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?
 
  • #5
Ray Vickson
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I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?
In your answer (2)(2) + (7)(-7), where did the 2 come from? What about the -2? Where did you get the 7? Ditto for the -7.

RGV
 
  • #6
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That answer looks correct to me. You are applying the 1. The equation for the derivative of the product of two functions is u*v' + v*u'. In your case, you have u(1)*v'(1) + v(1)*u'(1) = (2)(-2) + (7)(-7) = -53. This is d/dx(uv) evaluated at x=1.
 

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