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

The d/(dt)((x)(2acos(t)-acos(2t))dt) is xd(t(-2asin(t)+2asin(2t))+2acos(t)-acos(2t))

What is the first d/(dt)((x)(2acos(t)-acos(2t))dt) ?

The first d/(dt)((x)(2acos(t)-acos(2t))dt) is xd(t(-2asin(t)+2asin(2t))+2acos(t)-acos(2t))

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\frac{d}{d t} ((x) (2 a cos (t) - a cos (2 t)) d t)

x d (t (- 2 a sin (t) + 2 a sin (2 t)) + 2 a cos (t) - a cos (2 t))

Solution steps

\frac{d}{d t} ((x) (2 a cos (t) - a cos (2 t)) d t)

Treat

a, x, d

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = 2 a cos (t) - a cos (2 t), g = t

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

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

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

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

Simplify

= x d (t (- 2 a sin (t) + 2 a sin (2 t)) + 2 a cos (t) - a cos (2 t))

\frac{1}{( 4 x + 5 ) ^{3}}

\frac{0.0049}{( z - 1 ) ( 20 z - 19.6 ) ( 245 z - 227.85 )}

\frac{( 1 - 9 x ^{3} ) ( 5 - 4 x )}{( 2 + 3 x ) ( 1 - 8 x ^{2} )}

\frac{10}{( s - 1 ) ^{2}}

\frac{2 ( t - 10 ) ^{2}}{t}

What is the d/(dt)((x)(2acos(t)-acos(2t))dt) ?
The d/(dt)((x)(2acos(t)-acos(2t))dt) is xd(t(-2asin(t)+2asin(2t))+2acos(t)-acos(2t))
What is the first d/(dt)((x)(2acos(t)-acos(2t))dt) ?
The first d/(dt)((x)(2acos(t)-acos(2t))dt) is xd(t(-2asin(t)+2asin(2t))+2acos(t)-acos(2t))