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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (t)

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

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

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

Simplify

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

(sec (x))^{2} + (csc (x))^{2}

(x + 1) (x + 2) (x + 3) (x + 4) - 15

sin (π + π x)

1 + sin^{3} (y)

(x + y)^{2} + 8 (x + y) + 16

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