What is the (tsin(t))^' ?

The (tsin(t))^' is sin(t)+tcos(t)

What is the first (tsin(t))^' ?

The first (tsin(t))^' is sin(t)+tcos(t)

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(t sin (t))^{^{'}}

sin (t) + t cos (t)

Solution steps

(t sin (t))^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = sin (t)

= t^{^{'}} sin (t) + (sin (t))^{^{'}} t

t^{'} = 1

(sin (t))^{'} = cos (t)

= 1 \cdot sin (t) + cos (t) t

Simplify

= sin (t) + t cos (t)

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