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Popular >

d/(dt)((x)(1-sqrt(t)))

Solution

\frac{d}{d t} ((x) (1 - t))

Solution

\frac{d x}{d t} (1 - t) - \frac{x}{2 t}

Solution steps

\frac{d}{d t} ((x) (1 - t))

Apply the Product Rule:

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

f = x, g = 1 - t

= \frac{d x}{d t} (1 - t) + \frac{d}{d t} (1 - t) x

\frac{d}{d t} (1 - t) = - \frac{1}{2 t}

= \frac{d x}{d t} (1 - t) + (- \frac{1}{2 t}) x

Simplify

\frac{d x}{d t} (1 - t) + (- \frac{1}{2 t}) x : \frac{d x}{d t} (1 - t) - \frac{x}{2 t}

= \frac{d x}{d t} (1 - t) - \frac{x}{2 t}

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Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(1-sqrt(t))) ?
The d/(dt)((x)(1-sqrt(t))) is (dx)/(dt)(1-sqrt(t))-x/(2sqrt(t))
What is the first d/(dt)((x)(1-sqrt(t))) ?
The first d/(dt)((x)(1-sqrt(t))) is (dx)/(dt)(1-sqrt(t))-x/(2sqrt(t))