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

The d/(dt)((x)(cos(2t))) is cos(2t)(dx)/(dt)-2sin(2t)x

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

The first d/(dt)((x)(cos(2t))) is cos(2t)(dx)/(dt)-2sin(2t)x

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (2 t)

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

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

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

Simplify

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

(cos (θ))^{2}

(2 + x)^{3} - 8

b m^{2} + b y^{2} - c m^{2} - c y^{2}

π a^{2} - π b^{2}

3 (x)^{2}

What is the d/(dt)((x)(cos(2t))) ?
The d/(dt)((x)(cos(2t))) is cos(2t)(dx)/(dt)-2sin(2t)x
What is the first d/(dt)((x)(cos(2t))) ?
The first d/(dt)((x)(cos(2t))) is cos(2t)(dx)/(dt)-2sin(2t)x