anonymous
  • anonymous
If f(x)=xcosx , what does f"(x)=?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i am thinking it would be f"(x)=-cos
anonymous
  • anonymous
No, you need to use the product rule for that one because you're multiplying two different expressions of x. Do you know the product rule?
anonymous
  • anonymous
f(x)=(xcosx)(1-sin1)

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anonymous
  • anonymous
With the product rule, you take the first term and call it f(x) and then the second term and call it g(x), so we would have f(x)=x and g(x)=cosx. Then the formula for product rule is f ' (x)*g(x)+f(x)*g ' (x)
anonymous
  • anonymous
So the first derivative would be 1 * cosx + x * -sinx Does that make sense?
anonymous
  • anonymous
ok i think i am tracking
anonymous
  • anonymous
So f ' (x)=cosx-xsinx You were needing to go to the second derivative?
anonymous
  • anonymous
ok now i have to use the difference equation?
anonymous
  • anonymous
For the subtraction? Those derivatives can just be taken separately.
anonymous
  • anonymous
So you would take the derivative of cosx, which I'm sure you know how to do, and the derivative of -xsinx, which is the product rule again.
anonymous
  • anonymous
f"(x)=sinx+1*cosx+x*sinx ?
anonymous
  • anonymous
The derivative of cosx is -sinx. For the product rule, you would get -1*sinx-x*cosx So altogether it would be f '' (x) = -sinx-sinx-xcosx Or f '' (x) = -2sinx-xcosx
anonymous
  • anonymous
Can you see how I got that?
anonymous
  • anonymous
i am trying to work it all out as we speak
anonymous
  • anonymous
Sweetness i was able to work it out and it makes more sense now thanks a ton.
anonymous
  • anonymous
Not a problem.

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