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

The d/(dt)(tcos(2t)) is cos(2t)-2tsin(2t)

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

The first d/(dt)(tcos(2t)) is cos(2t)-2tsin(2t)

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

cos (2 t) - 2 t sin (2 t)

Solution steps

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

Apply the Product Rule:

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

f = t, g = cos (2 t)

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

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

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

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

Simplify

= cos (2 t) - 2 t sin (2 t)

4 x + \frac{1}{x}

x sin (x^{2}) y^{^{'}} + y (4 x^{2} cos (x^{2}) - sin (x^{2})) = 0

\int x^{2} + 25 d x

\int \frac{3}{9 - x ^{2}} d x

\frac{d}{d x} ((3 x^{6} + 8 x^{3})^{4})

What is the d/(dt)(tcos(2t)) ?
The d/(dt)(tcos(2t)) is cos(2t)-2tsin(2t)
What is the first d/(dt)(tcos(2t)) ?
The first d/(dt)(tcos(2t)) is cos(2t)-2tsin(2t)