What is the d/(dt)((h(t))(-{g}(t))) ?

The d/(dt)((h(t))(-{g}(t))) is h(-{g}(t)-t d/(dt)({g}(t)))

What is the first d/(dt)((h(t))(-{g}(t))) ?

The first d/(dt)((h(t))(-{g}(t))) is h(-{g}(t)-t d/(dt)({g}(t)))

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\frac{d}{d t} ((h (t)) (- g (t)))

h (- g (t) - t \frac{d}{d t} (g (t)))

Solution steps

\frac{d}{d t} ((h (t)) (- g (t)))

Treat

h

as a constant

Take the constant out:

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

= h \frac{d}{d t} (t (- g (t)))

Apply the Product Rule:

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

f = t, g = - g (t)

= h (\frac{d t}{d t} (- g (t)) + \frac{d}{d t} (- g (t)) t)

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

\frac{d}{d t} (- g (t)) = - \frac{d}{d t} (g (t))

= h (1 \cdot (- g (t)) + (- \frac{d}{d t} (g (t))) t)

Simplify

= h (- g (t) - t \frac{d}{d t} (g (t)))

[- 12]

(x + y)^{3} + 1

\frac{e ^{2} - 1}{e ^{2}}

88 m^{6} e^{4} - 20 m^{5}

x^{3} - 6 x^{2} + 8 x d x

What is the d/(dt)((h(t))(-{g}(t))) ?
The d/(dt)((h(t))(-{g}(t))) is h(-{g}(t)-t d/(dt)({g}(t)))
What is the first d/(dt)((h(t))(-{g}(t))) ?
The first d/(dt)((h(t))(-{g}(t))) is h(-{g}(t)-t d/(dt)({g}(t)))