Math Is Fun Forum

Neela

Guest

calculus

Hey!

Given that y=sinx(1-cosx) show that

dy/dx = (1+ 2 cos x)(1 - cos x)

I cant get this to fit :-(

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: calculus

To differentiate this you need to use the product rule. Basically, you differentiate the first term and multiply that by the second, then you differentiate the second term and multiply that by the first and add both the results together.

In this case, you get that dy/dx = cosx(1 - cosx) + sinx(sinx) = cosx(1 - cosx) +sin²x

Now you just need to manipulate that to get it into the form you want.
sin²x is the same as (1 - cos²x).
(1 - cos²x) is a difference of 2 squares and so can be written as (1 + cosx)(1 - cosx).

So now we have cosx(1 - cosx) + (1 + cosx)(1 - cosx)
This can be factorised into (1 - cosx)(cosx + 1 + cosx), which is (1 + 2cosx)(1 - cosx).

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Why did the vector cross the road?
It wanted to be normal.

Neela

Guest

Re: calculus

Thanks a bunch