Differentiate with respect to t

Question

anonymous · Answer

$$y=d \cos t + t^2 \sin t$$

mathmale · Answer

Did you mean for that 'd' to be in there?

What is the derivative of the cosine function?

(t^2)(sin t) is a PRODUCT first and foremost.  How do you differentiate a product?

anonymous · Answer

yes, 
the derivative of cos is -sint

anonymous · Answer

i don't remember how to differentiate a product :( 
is it fg=g'f+f'g?

mathmale · Answer

Fine.  You're on your way.
Yes, that's correct as the product rule.  Label it (fg).

mathmale · Answer

What is the derivative of t^2?
What is the derivative of cos t?

anonymous · Answer

derivative of t^2 is
2t

derivative of cost is 
-sint

mathmale · Answer

OK, then.  What is the deriv. of (t^2)(sin t)?

(                            )(                            ) +    (                   )(                   )

mathmale · Answer

(          t^2                  )(              ?              ) +    (         ?          )(         ?          )

mathmale · Answer

I think you're well on the way to finding the overall derivative.  I need to get off the 'Net pretty quick.

anonymous · Answer

[(-sin t)(d) + (1)(cos t)] + [(cos t)(t^2)+(2t)(sin t)]

anonymous · Answer

ohhh ok

mathmale · Answer

dy/dt = (              ) + (  t^2)(                      )+ (                     )(                        )

Looks good .   Do check it once more.  Should have FIVE terms, incl. the d*(-sin t) term.
I'd be happy to continue later if  you like.

Glad to work with you!

anonymous · Answer

thank you!!