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Popular >

d/(dt)((x)(cos(t)+tsin(t)))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (t) + t sin (t)

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

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

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

Popular Examples

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Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(cos(t)+tsin(t))) ?
The d/(dt)((x)(cos(t)+tsin(t))) is (dx)/(dt)(cos(t)+tsin(t))+tcos(t)x
What is the first d/(dt)((x)(cos(t)+tsin(t))) ?
The first d/(dt)((x)(cos(t)+tsin(t))) is (dx)/(dt)(cos(t)+tsin(t))+tcos(t)x