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# Differentiation Help Watch

Any ideas of how you would differentiate $y = 10sin\binom{\pi 19}{12}$?.

Is it y = -20 cos (pi x 19 / 12)?

Cheers
2. Are you sure the equation came out right or is it supposed to look like something else?
3. the question is: find dy/dt and calculate the rate of change when t = 19. The original equation was: y = 10sin (pi x t / 12).
4. (Original post by Slicksomnia)

Any ideas of how you would differentiate $y = 10sin\binom{\pi 19}{12}$?.

Is it y = -20 cos (pi x 19 / 12)?

Cheers
Do you mean ?

If so, use:

where

Then:

This is the 'chain rule'.

If you don't mean that...clarify?

EDIT: Oh, you already did clarify. In that case:

where

And you can still use the chain rule to solve it.

To find the rate of change at t = 19, remember that differentiation gives the rate of change, so you just put t=19 into your new equation.

You cannot put t=19 straight into your first equation (like you tried to), that doesn't make any sense. You have a function for y in terms of t. To find the rate of change, you differentiate y with respect to t. This new equation is the one you must substitute t=19 into.
5. (Original post by dring)
Do you mean ?

If so, use:

where

Then:

This is the 'chain rule'.

If you don't mean that...clarify?

EDIT: Oh, you already did clarify. In that case:

where

And you can still use the chain rule to solve it.

To find the rate of change at t = 19, remember that differentiation gives the rate of change, so you just put t=19 into your new equation.

You cannot put t=19 straight into your first equation (like you tried to), that doesn't make any sense. You have a function for y in terms of t. To find the rate of change, you differentiate y with respect to t. This new equation is the one you must substitute t=19 into.
Thanks for the help. I think I worked it out correctly.

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Updated: December 8, 2010
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