What is the d/(dt)(({Q}(t))k({Q}(t)-70)) ?

The d/(dt)(({Q}(t))k({Q}(t)-70)) is k(2{Q}(t) d/(dt)({Q}(t))-70 d/(dt)({Q}(t)))

What is the first d/(dt)(({Q}(t))k({Q}(t)-70)) ?

The first d/(dt)(({Q}(t))k({Q}(t)-70)) is k(2{Q}(t) d/(dt)({Q}(t))-70 d/(dt)({Q}(t)))

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\frac{d}{d t} ((Q (t)) k (Q (t) - 70))

k (2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t)))

Solution steps

\frac{d}{d t} ((Q (t)) k (Q (t) - 70))

Take the constant out:

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

= k \frac{d}{d t} (Q (t) (Q (t) - 70))

Apply the Product Rule:

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

f = Q (t), g = Q (t) - 70

= k (\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t) - 70) Q (t))

\frac{d}{d t} (Q (t) - 70) = \frac{d}{d t} (Q (t))

= k (\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t)) Q (t))

Expand

\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t)) Q (t) : 2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t))

= k (2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t)))

(3 x + 2 i)^{2}

\frac{2 x + 5}{( x ^{2} + 2 ) ( x + 1 ) ^{''}}

(2 x + 1)!

(\frac{x ^{2} y ^{3}}{3} - 6) (\frac{x ^{2} y ^{3}}{3} + 8)

(0.6 \times \frac{20}{7} + \frac{3}{14}) \times 1.5

What is the d/(dt)(({Q}(t))k({Q}(t)-70)) ?
The d/(dt)(({Q}(t))k({Q}(t)-70)) is k(2{Q}(t) d/(dt)({Q}(t))-70 d/(dt)({Q}(t)))
What is the first d/(dt)(({Q}(t))k({Q}(t)-70)) ?
The first d/(dt)(({Q}(t))k({Q}(t)-70)) is k(2{Q}(t) d/(dt)({Q}(t))-70 d/(dt)({Q}(t)))