Differentiation

Hi all, I'm facing a problem in this differentiation question. Please help me solve it. Thanks so much. :)


y = (cos^2x)/ x

Are you wanting the derivative?

The derivative can be easily solved using the product rule, but simply changing it around some to look like:

cos^2(x) * x^-1

Once you have it like that your only real problem is that you don't know the derivative of cos^2(x), so looking that up I find it is...

-2cos(x)sin(x)

Armed with that knowledge you should be able to differentiate.

Quote:

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Originally Posted by dsheller

The derivative can be easily solved using the product rule, but simply changing it around some to look like:

cos^2(x) * x^-1

Once you have it like that your only real problem is that you don't know the derivative of cos^2(x), so looking that up I find it is...

-2cos(x)sin(x)

Armed with that knowledge you should be able to differentiate.

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:ehh: I have tried using the product rule to solve it. But then, my answer is different from the textbook answer. Could you please help me check out whether my answer is correct? Thank you. :)

My answer is -(2xsinx - cos^2x)/x^2
The Textbook answer is -(2xsinx cosx + cos^2x)/x^2

I think you need to re-check the derivative of cos²(x). I agree with your textbook. Actually, dsheller already provided the answer.:)