What is the d/(dt)((x)(0.2xt)) ?

The d/(dt)((x)(0.2xt)) is 0.2(x^2+2tx(dx)/(dt))

What is the first d/(dt)((x)(0.2xt)) ?

The first d/(dt)((x)(0.2xt)) is 0.2(x^2+2tx(dx)/(dt))

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\frac{d}{d t} ((x) (0.2 x t))

0.2 (x^{2} + 2 t x \frac{d x}{d t})

Solution steps

\frac{d}{d t} ((x) (0.2 x t))

Simplify

(x) (0.2 x t) : 0.2 t x^{2}

= \frac{d}{d t} (0.2 t x^{2})

Take the constant out:

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

= 0.2 \frac{d}{d t} (t x^{2})

Apply the Product Rule:

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

f = t, g = x^{2}

= 0.2 (\frac{d t}{d t} x^{2} + \frac{d}{d t} (x^{2}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (x^{2}) = 2 x \frac{d x}{d t}

= 0.2 (1 \cdot x^{2} + 2 x \frac{d x}{d t} t)

Simplify

= 0.2 (x^{2} + 2 t x \frac{d x}{d t})

2 b^{2} c - 6 b^{2} d + 5 x c - 15 x d

- (2^{\frac{1}{3}})

u - 12 u^{- 1} - 1

8 x^{3 + 27}

2 - (\frac{- 3 + 97}{2})

What is the d/(dt)((x)(0.2xt)) ?
The d/(dt)((x)(0.2xt)) is 0.2(x^2+2tx(dx)/(dt))
What is the first d/(dt)((x)(0.2xt)) ?
The first d/(dt)((x)(0.2xt)) is 0.2(x^2+2tx(dx)/(dt))