Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to figure out the derivative of $y= \frac{t\sin t}{1+t}$ I know the quotient rules are needed but I think what is confusing is some fairly simple math. Here is what I did.

(1+t)(tcost) - (tsint)(1) this could be wrong but I think it is correct. Anyways what I was confused on was multiplying t into tcost. I forget the rules but is tcost times t should be $t^2\cos$ or something close but I am not sure. Anyways I end up with $ \frac{t\cos t+t^2 \cos t - t \sin t}{(1+t)^2}$ but this is not correct.

share|improve this question
    
Currently you have $1+\sec \theta$ at the bottom. Is that intended? –  André Nicolas Sep 22 '11 at 14:57
    
I fixed it, that should be the correct problem now. I don't understand what $t\cos\,t\tan\frac{t}{2}$ is –  user138246 Sep 22 '11 at 15:00
    
You almost did it right. The "I think it is correct" part is not. You want $(1+t)$ times the derivative of $t\sin t$ minus $t\sin t$. The derivative of $t\sin t$ is not $t\cos t$, it is $t\cos t +\sin t$ (product rule). –  André Nicolas Sep 22 '11 at 15:13
    
I don't really know what you are trying to say, but is my derivative of tsint wrong? Thinking about it now it should be the derivative of tsint which would be sint(1) + cost(t) is that correct? –  user138246 Sep 22 '11 at 15:15
    
"but is my derivative of tsint wrong" - Yes, exactly. And $\sin t (1) + \cos t (t)$ is correct derivative of $t \sin t$. –  Srivatsan Sep 22 '11 at 15:23
show 3 more comments

1 Answer

up vote 1 down vote accepted

The product and quotient rules need to be used here. For example, we can first use the product rule $$ \begin{align} \frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{t\sin(t)}{1+t}\right) &=\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{t}{1+t}\sin(t)\right)\\ &=\left(\frac{\mathrm{d}}{\mathrm{d}t}\frac{t}{1+t}\right)\sin(t)+\frac{t}{1+t}\left(\frac{\mathrm{d}}{\mathrm{d}t}\sin(t)\right) \end{align} $$ and then use the quotient rule for $\frac{\mathrm{d}}{\mathrm{d}t}\frac{t}{1+t}$. Alternatively, there is nothing wrong with using the quotient rule first and then using the product rule for $\frac{\mathrm{d}}{\mathrm{d}t}(t\sin(t))$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.