What is the d/(dt)((r)(rcos(t))) ?

The d/(dt)((r)(rcos(t))) is -sin(t)r^2+2cos(t)r(dr)/(dt)

What is the first d/(dt)((r)(rcos(t))) ?

The first d/(dt)((r)(rcos(t))) is -sin(t)r^2+2cos(t)r(dr)/(dt)

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

- sin (t) r^{2} + 2 cos (t) r \frac{d r}{d t}

Solution steps

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

Simplify

(r) (r cos (t)) : cos (t) r^{2}

= \frac{d}{d t} (cos (t) r^{2})

Apply the Product Rule:

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

f = cos (t), g = r^{2}

= \frac{d}{d t} (cos (t)) r^{2} + \frac{d}{d t} (r^{2}) cos (t)

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

\frac{d}{d t} (r^{2}) = 2 r \frac{d r}{d t}

= (- sin (t)) r^{2} + 2 r \frac{d r}{d t} cos (t)

Simplify

= - sin (t) r^{2} + 2 cos (t) r \frac{d r}{d t}

\frac{5}{7} - \frac{2}{3}

125 x^{3} - 27 x^{3}

x^{3} - 3 x^{2} 4 x + 12

y^{2} - y^{2}

x^{(n - 1)}

What is the d/(dt)((r)(rcos(t))) ?
The d/(dt)((r)(rcos(t))) is -sin(t)r^2+2cos(t)r(dr)/(dt)
What is the first d/(dt)((r)(rcos(t))) ?
The first d/(dt)((r)(rcos(t))) is -sin(t)r^2+2cos(t)r(dr)/(dt)