What is the d/(dt)(tsin(t)) ?

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

What is the first d/(dt)(tsin(t)) ?

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

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

sin (t) + t cos (t)

Solution steps

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

Apply the Product Rule:

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

f = t, g = sin (t)

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

\frac{d t}{d t} = 1

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

= 1 \cdot sin (t) + cos (t) t

Simplify

= sin (t) + t cos (t)

\int - \frac{2 x}{( 1 - x ^{2} )} d x

\frac{d x}{d y} = \frac{4 x}{9 y}

y y^{^{'}} + 6 x = 0

\int x^{2} (x^{3} - 4)^{4} d x

\int 3^{- x} cos (x) d x