What is the d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) ?

The d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) is

What is the first d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) ?

The first d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) is

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\frac{d}{d t} (t - 2 (t - 1) u_{(1)} (t) (t) + (t - 2) u_{(2)} (t) (t) (t))

1 - 2 (t^{2} \frac{d}{d t} (u_{(1)} (t)) + 2 t u_{(1)} (t) - t \frac{d}{d t} (u_{(1)} (t)) - u_{(1)} (t)) + t^{3} \frac{d}{d t} (u_{(2)} (t)) + 3 t^{2} u_{(2)} (t) - 2 t^{2} \frac{d}{d t} (u_{(2)} (t)) - 4 t u_{(2)} (t)

Solution steps

\frac{d}{d t} (t - 2 (t - 1) u_{(1)} (t) (t) + (t - 2) u_{(2)} (t) (t) (t))

Simplify

t - 2 (t - 1) u_{(1)} (t) (t) + (t - 2) u_{(2)} (t) (t) (t) : t - 2 t (t - 1) u_{(1)} (t) + t^{2} (t - 2) u_{(2)} (t)

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d t} (t^{2} (t - 2) u_{(2)} (t)) = t^{3} \frac{d}{d t} (u_{(2)} (t)) + 3 t^{2} u_{(2)} (t) - 2 t^{2} \frac{d}{d t} (u_{(2)} (t)) - 4 t u_{(2)} (t)

= 1 - 2 (t^{2} \frac{d}{d t} (u_{(1)} (t)) + 2 t u_{(1)} (t) - t \frac{d}{d t} (u_{(1)} (t)) - u_{(1)} (t)) + t^{3} \frac{d}{d t} (u_{(2)} (t)) + 3 t^{2} u_{(2)} (t) - 2 t^{2} \frac{d}{d t} (u_{(2)} (t)) - 4 t u_{(2)} (t)

sin (4 t) cos (3 t)

\frac{d}{d x} ((1 + 2 x)^{\frac{1}{2}})

t + 3

\int 10 x - 3 d x

y = \frac{1}{x}, y = x, y = \frac{x}{4}

What is the d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) ?
The d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) is
What is the first d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) ?
The first d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t)) is