What is the d/(dt)(tsin(2t)) ?

The d/(dt)(tsin(2t)) is sin(2t)+2tcos(2t)

What is the first d/(dt)(tsin(2t)) ?

The first d/(dt)(tsin(2t)) is sin(2t)+2tcos(2t)

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\frac{d}{d t} (t sin (2 t))

sin (2 t) + 2 t cos (2 t)

Solution steps

\frac{d}{d t} (t sin (2 t))

Apply the Product Rule:

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

f = t, g = sin (2 t)

= \frac{d t}{d t} sin (2 t) + \frac{d}{d t} (sin (2 t)) t

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

\frac{d}{d t} (sin (2 t)) = cos (2 t) \cdot 2

= 1 \cdot sin (2 t) + cos (2 t) \cdot 2 t

Simplify

= sin (2 t) + 2 t cos (2 t)

\frac{\partial}{\partial v} (v \cdot e^{u (v)})

f (2) = sin (3 x) - 4 x^{4} + 2 x^{3} + 3

\int cos (x) (2 + 4 sin^{2} (x)) d x

f (x) = \frac{2 x}{1 + x ^{2}}, at x = (4)

x y^{^{'}} - 2 y = x^{4}, y (1) = 0

What is the d/(dt)(tsin(2t)) ?
The d/(dt)(tsin(2t)) is sin(2t)+2tcos(2t)
What is the first d/(dt)(tsin(2t)) ?
The first d/(dt)(tsin(2t)) is sin(2t)+2tcos(2t)