What is the d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) ?

The d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) is a_{2}(cos(2t)-2tsin(2t))+a_{2}(sin(2t)+2tcos(2t))

What is the first d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) ?

The first d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) is a_{2}(cos(2t)-2tsin(2t))+a_{2}(sin(2t)+2tcos(2t))

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

a_{2} (cos (2 t) - 2 t sin (2 t)) + a_{2} (sin (2 t) + 2 t cos (2 t))

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= a_{2} (cos (2 t) - 2 t sin (2 t)) + a_{2} (sin (2 t) + 2 t cos (2 t))

\int 1

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} - x^{\frac{2}{3}} + 1)

\int \frac{1 - u ^{2}}{u + u ^{3}} d u

\int 12 x^{2} + e^{x} d x

\frac{d}{d x} (ln (arctan (4 x^{3})))

What is the d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) ?
The d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) is a_{2}(cos(2t)-2tsin(2t))+a_{2}(sin(2t)+2tcos(2t))
What is the first d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) ?
The first d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t)) is a_{2}(cos(2t)-2tsin(2t))+a_{2}(sin(2t)+2tcos(2t))