What is the d/(dt)({r}(t)cos(t)) ?

The d/(dt)({r}(t)cos(t)) is cos(t) d/(dt)({r}(t))-sin(t){r}(t)

What is the first d/(dt)({r}(t)cos(t)) ?

The first d/(dt)({r}(t)cos(t)) is cos(t) d/(dt)({r}(t))-sin(t){r}(t)

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\frac{d}{d t} (r (t) cos (t))

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

Solution steps

\frac{d}{d t} (r (t) cos (t))

Apply the Product Rule:

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

f = r (t), g = cos (t)

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

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

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

Simplify

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

What is the d/(dt)({r}(t)cos(t)) ?
The d/(dt)({r}(t)cos(t)) is cos(t) d/(dt)({r}(t))-sin(t){r}(t)
What is the first d/(dt)({r}(t)cos(t)) ?
The first d/(dt)({r}(t)cos(t)) is cos(t) d/(dt)({r}(t))-sin(t){r}(t)