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i am thinking it would be f"(x)=-cos
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?
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)
So the first derivative would be 1 * cosx + x * -sinx Does that make sense?
ok i think i am tracking
So f ' (x)=cosx-xsinx You were needing to go to the second derivative?
ok now i have to use the difference equation?
For the subtraction? Those derivatives can just be taken separately.
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.
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
Can you see how I got that?
i am trying to work it all out as we speak
Sweetness i was able to work it out and it makes more sense now thanks a ton.
Not a problem.