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

The d/(dt)((x)(t-sin(t))) is (dx)/(dt)(t-sin(t))+(1-cos(t))x

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

The first d/(dt)((x)(t-sin(t))) is (dx)/(dt)(t-sin(t))+(1-cos(t))x

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\frac{d}{d t} ((x) (t - sin (t)))

\frac{d x}{d t} (t - sin (t)) + (1 - cos (t)) x

Solution steps

\frac{d}{d t} ((x) (t - sin (t)))

Apply the Product Rule:

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

f = x, g = t - sin (t)

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

\frac{d}{d t} (t - sin (t)) = 1 - cos (t)

= \frac{d x}{d t} (t - sin (t)) + (1 - cos (t)) x

(3 + 2 i) (3 - 2 i)

\frac{2 s + 8}{s ( s ^{2} + 2 s + 4 )}

\frac{6 x - x ^{2}}{( x + 3 ) ^{2}}

\frac{6 ( s + 3 )}{s ( s + 1 ) ( s + 2 )}

(1 + 2) x

What is the d/(dt)((x)(t-sin(t))) ?
The d/(dt)((x)(t-sin(t))) is (dx)/(dt)(t-sin(t))+(1-cos(t))x
What is the first d/(dt)((x)(t-sin(t))) ?
The first d/(dt)((x)(t-sin(t))) is (dx)/(dt)(t-sin(t))+(1-cos(t))x