What is the -d/(dt)(sin(2t)) ?

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

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Find the Derivative - d/dt sin(2t)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

: t \frac{d}{d t} (sin (2 t)) - \int - 4 t sin (2 t) d t

= - (t \frac{d}{d t} (sin (2 t)) - \int - 4 t sin (2 t) d t)

\int - 4 t sin (2 t) d t = 2 t cos (2 t) - sin (2 t)

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

Simplify

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

Add a constant to the solution

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

- \frac{d}{d x} y = 3 e^{x}

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

- \frac{d}{d x} f (x) = e^{6 x}

f (x) = sin (2 x)

f (x) = \frac{1}{( x ^{3} )}

What is the -d/(dt)(sin(2t)) ?
The -d/(dt)(sin(2t)) is -t d/(dt)(sin(2t))+2tcos(2t)-sin(2t)+C