What is the d/(dt)((x)(5cos(t))) ?

The d/(dt)((x)(5cos(t))) is 5(cos(t)(dx)/(dt)-sin(t)x)

What is the first d/(dt)((x)(5cos(t))) ?

The first d/(dt)((x)(5cos(t))) is 5(cos(t)(dx)/(dt)-sin(t)x)

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\frac{d}{d t} ((x) (5 cos (t)))

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

Solution steps

\frac{d}{d t} ((x) (5 cos (t)))

Take the constant out:

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

= 5 \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)

= 5 (\frac{d x}{d t} cos (t) + \frac{d}{d t} (cos (t)) x)

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

= 5 (\frac{d x}{d t} cos (t) + (- sin (t)) x)

Simplify

= 5 (cos (t) \frac{d x}{d t} - sin (t) x)

216 a^{3} + b^{6} c^{9}

(6 x - 1) + (- x^{2})

(x^{- 1} + y^{- 1})^{2}

a^{4} + 6^{2} + 1

(x^{2} y^{4}) 2

What is the d/(dt)((x)(5cos(t))) ?
The d/(dt)((x)(5cos(t))) is 5(cos(t)(dx)/(dt)-sin(t)x)
What is the first d/(dt)((x)(5cos(t))) ?
The first d/(dt)((x)(5cos(t))) is 5(cos(t)(dx)/(dt)-sin(t)x)