What is the d/(dt)((t)(k(t-M))) ?

The d/(dt)((t)(k(t-M))) is k(2t-M)

What is the first d/(dt)((t)(k(t-M))) ?

The first d/(dt)((t)(k(t-M))) is k(2t-M)

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\frac{d}{d t} ((t) (k (t - M)))

k (2 t - M)

Solution steps

\frac{d}{d t} ((t) (k (t - M)))

Treat

k, M

as a constant

Take the constant out:

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

= k \frac{d}{d t} (t (t - M))

Apply the Product Rule:

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

f = t, g = t - M

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

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

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

= k (1 \cdot (t - M) + 1 \cdot t)

Simplify

k (1 \cdot (t - M) + 1 \cdot t) : k (2 t - M)

= k (2 t - M)

(3 x + y - 2 z)^{5}

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10 (a - 5 = 6 (a - 3))

\frac{7 x ( 4 x + 7 )}{( 7 x - 4 ) ^{2}}

\frac{( x ^{2} - 1 ) e ^{x^{2}}}{2}

What is the d/(dt)((t)(k(t-M))) ?
The d/(dt)((t)(k(t-M))) is k(2t-M)
What is the first d/(dt)((t)(k(t-M))) ?
The first d/(dt)((t)(k(t-M))) is k(2t-M)