What is the d/(dt)(({r}(t,y,x))(y+xcos(t))) ?

The d/(dt)(({r}(t,y,x))(y+xcos(t))) is d/(dt)({r}(t,y,x))(y+xcos(t))+(-xsin(t)){r}(t,y,x)

What is the first d/(dt)(({r}(t,y,x))(y+xcos(t))) ?

The first d/(dt)(({r}(t,y,x))(y+xcos(t))) is d/(dt)({r}(t,y,x))(y+xcos(t))+(-xsin(t)){r}(t,y,x)

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\frac{d}{d t} ((r (t, y, x)) (y + x cos (t)))

\frac{d}{d t} (r (t, y, x)) (y + x cos (t)) + (- x sin (t)) r (t, y, x)

Solution steps

\frac{d}{d t} ((r (t, y, x)) (y + x cos (t)))

Treat

y, x

as constants

Apply the Product Rule:

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

f = r (t, y, x), g = y + x cos (t)

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

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

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

\frac{9}{x ( x + 6 )}

\frac{( 5 x - 5 )}{5} \cdot \frac{( x + 10 )}{( x - 1 )}

(π + 2) (2 - 1)

\frac{( x ^{3} + 4 x ^{2} + x - 6 )}{x + 3}

\frac{7 ( 3 - 3 z ) ^{2}}{2}

What is the d/(dt)(({r}(t,y,x))(y+xcos(t))) ?
The d/(dt)(({r}(t,y,x))(y+xcos(t))) is d/(dt)({r}(t,y,x))(y+xcos(t))+(-xsin(t)){r}(t,y,x)
What is the first d/(dt)(({r}(t,y,x))(y+xcos(t))) ?
The first d/(dt)(({r}(t,y,x))(y+xcos(t))) is d/(dt)({r}(t,y,x))(y+xcos(t))+(-xsin(t)){r}(t,y,x)