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Popular >

d/(dt)((x)(4t-x))

Solution

\frac{d}{d t} ((x) (4 t - x))

Solution

4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

Solution steps

\frac{d}{d t} ((x) (4 t - x))

Apply the Product Rule:

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

f = x, g = 4 t - x

= \frac{d x}{d t} (4 t - x) + \frac{d}{d t} (4 t - x) x

\frac{d}{d t} (4 t - x) = 4 - \frac{d x}{d t}

= \frac{d x}{d t} (4 t - x) + (4 - \frac{d x}{d t}) x

Simplify

\frac{d x}{d t} (4 t - x) + (4 - \frac{d x}{d t}) x : 4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

= 4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

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Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(4t-x)) ?
The d/(dt)((x)(4t-x)) is 4t(dx)/(dt)-2x(dx)/(dt)+4x
What is the first d/(dt)((x)(4t-x)) ?
The first d/(dt)((x)(4t-x)) is 4t(dx)/(dt)-2x(dx)/(dt)+4x