What is the d/(dt)(sin(t)+tcos(t)) ?

The d/(dt)(sin(t)+tcos(t)) is 2cos(t)-tsin(t)

What is the first d/(dt)(sin(t)+tcos(t)) ?

The first d/(dt)(sin(t)+tcos(t)) is 2cos(t)-tsin(t)

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\frac{d}{d t} (sin (t) + t cos (t))

2 cos (t) - t sin (t)

Solution steps

\frac{d}{d t} (sin (t) + t cos (t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (sin (t)) + \frac{d}{d t} (t cos (t))

\frac{d}{d t} (sin (t)) = cos (t)

\frac{d}{d t} (t cos (t)) = cos (t) - t sin (t)

= cos (t) + cos (t) - t sin (t)

Simplify

= 2 cos (t) - t sin (t)

What is the d/(dt)(sin(t)+tcos(t)) ?
The d/(dt)(sin(t)+tcos(t)) is 2cos(t)-tsin(t)
What is the first d/(dt)(sin(t)+tcos(t)) ?
The first d/(dt)(sin(t)+tcos(t)) is 2cos(t)-tsin(t)