SOLUTION
We want to find the derivative of
[tex]y=sin(1.2t-3.7)[/tex]
(a) So, using chain rule, the inside function is u,
we have the inside:
[tex]u=1.2t-3.7[/tex]
outside becomes
[tex]y=sin(u)[/tex]
(b) The derivative of
inside, we have
[tex]\frac{du}{dt}=1.2[/tex]
derivative of the outside, we have
[tex]\frac{dy}{du}=cos(u)[/tex]
chain rule we have
[tex]\begin{gathered} \frac{dy}{dt}=\frac{dy}{du}\times\frac{du}{dt} \\ =cos(u)\times1.2 \\ =cos(1.2t-3.7)\times1.2 \end{gathered}[/tex]
Hence the answer is
[tex]\frac{dy}{dt}=1.2cos(1.2t-3.7)[/tex]
