Question

Help with taking derivative of trig function

Answer 1

10sin120pit

Answer 2

For clarity I'm re-writing your function, 10sin120pit:

\[y=10\sin120 \pi t\]

Answer 3

The main function here is the sine. Here its argument is another function, namely, 120 pi t. Thus your overall function is a composite function.

You must first find the derivative of y with respect to 120 pi t and then find the derivative of 120 pi t with respect to t. Would you try this, please, sharing all of your work here?

Answer 4

Once more: Find the derivative of sin u with respect to u, and then multiply that by the derivative of u with respect to t:

\[\frac{ dy }{ dt }=10 \cos 120 \pi t*\frac{ d }{ dt }120 \pi t\]