Question

If f(x)=xcosx , what does f"(x)=?

Answer 1

i am thinking it would be f"(x)=-cos

Answer 2

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?

Answer 3

f(x)=(xcosx)(1-sin1)

Answer 4

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)

Answer 5

So the first derivative would be 1 * cosx + x * -sinx

Does that make sense?

Answer 6

ok i think i am tracking

Answer 7

So f ' (x)=cosx-xsinx

You were needing to go to the second derivative?

Answer 8

ok now i have to use the difference equation?

Answer 9

For the subtraction? Those derivatives can just be taken separately.

Answer 10

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.

Answer 11

f"(x)=sinx+1*cosx+x*sinx ?

Answer 12

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

Answer 13

Can you see how I got that?

Answer 14

i am trying to work it all out as we speak

Answer 15

Sweetness i was able to work it out and it makes more sense now thanks a ton.

Answer 16

Not a problem.