Question

y=cos (5-3t), dy/dt =?

Answer 1

your answer is 3sin(5-3t)

Answer 2

Hope u like my process
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We know,

$= > \bf \: \frac{d( \cos( \alpha ) )}{d \alpha } = - \sin( \alpha ) \\ \\ = > \frac{d(4 - 5 \alpha )}{d \alpha } = - 5$
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Now,

$= > y = \cos(5- 3t) \\ \\ \bf \: let \: \: 5 - 3t = z \\ \\ \bf \underline{ \: differentiating \: \: both \: \: sides \: with \: respect \: to \: \: t \: \: we \: \: get} \\ \\ = > - 3 = \frac{dz}{dt} \\ \\ \bf \: \: \: \: \: \: \: \: now \\ \\ = > \frac{dy}{dt} = \frac{d( \cos(z) )}{dt} = - \sin(z) \frac{dz}{dt} \\ \\ = > \bf \: \frac{dy}{dt} = - \sin(5 - 3t) \times ( - 3) = \underline{3\sin(5 - 3t) }$
Hope this is ur required answer

Proud to help you