What is the d/(dt)(({r}(t))(cos(5t))) ?

The d/(dt)(({r}(t))(cos(5t))) is cos(5t) d/(dt)({r}(t))-5sin(5t){r}(t)

What is the first d/(dt)(({r}(t))(cos(5t))) ?

The first d/(dt)(({r}(t))(cos(5t))) is cos(5t) d/(dt)({r}(t))-5sin(5t){r}(t)

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\frac{d}{d t} ((r (t)) (cos (5 t)))

cos (5 t) \frac{d}{d t} (r (t)) - 5 sin (5 t) r (t)

Solution steps

\frac{d}{d t} ((r (t)) (cos (5 t)))

Apply the Product Rule:

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

f = r (t), g = cos (5 t)

= \frac{d}{d t} (r (t)) cos (5 t) + \frac{d}{d t} (cos (5 t)) r (t)

\frac{d}{d t} (cos (5 t)) = - sin (5 t) \cdot 5

= \frac{d}{d t} (r (t)) cos (5 t) + (- sin (5 t) \cdot 5) r (t)

Simplify

= cos (5 t) \frac{d}{d t} (r (t)) - 5 sin (5 t) r (t)

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n r - 6 n + m r - 6 m

x^{2} + x - x^{3} y - y

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What is the d/(dt)(({r}(t))(cos(5t))) ?
The d/(dt)(({r}(t))(cos(5t))) is cos(5t) d/(dt)({r}(t))-5sin(5t){r}(t)
What is the first d/(dt)(({r}(t))(cos(5t))) ?
The first d/(dt)(({r}(t))(cos(5t))) is cos(5t) d/(dt)({r}(t))-5sin(5t){r}(t)