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

The d/(dt)((t)(-k(t-ta))) is -2kt+2akt

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

The first d/(dt)((t)(-k(t-ta))) is -2kt+2akt

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

- 2 k t + 2 ak t

Solution steps

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

Apply the Product Rule:

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

f = t, g = - k (t - t a)

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

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

\frac{d}{d t} (- k (t - t a)) = - k (1 - a)

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

Simplify

1 \cdot (- k (t - t a)) + (- k (1 - a)) t : - 2 k t + 2 ak t

= - 2 k t + 2 ak t

x (3 x - 2 y = 0)

- 8 x^{7} y^{4} (- 2 x y + 4 x, y^{5})

(3 - x) - 1

(t - π) e^{(2 t)} u (t) cos (3 t)

d x (x^{2} + y^{2} = 0)

What is the d/(dt)((t)(-k(t-ta))) ?
The d/(dt)((t)(-k(t-ta))) is -2kt+2akt
What is the first d/(dt)((t)(-k(t-ta))) ?
The first d/(dt)((t)(-k(t-ta))) is -2kt+2akt