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

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

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

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

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

- x^{2} - 2 t x \frac{d x}{d t}

Solution steps

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

Simplify

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

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

Take the constant out:

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

= - \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}

= - (\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}

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

Simplify

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

= - x^{2} - 2 t x \frac{d x}{d t}

\frac{x + 5}{x ^{3} + 125}

A e^{2 x} + B e^{- 2 x}

27 (h + 2)^{9} - k^{15} r^{3}

\frac{- 5 + 5 41}{2}

7 5 + 105

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