What is the d/(dt)(({x}(t,s))(s+t)) ?

The d/(dt)(({x}(t,s))(s+t)) is d/(dt)({x}(t,s))(s+t)+1*{x}(t,s)

What is the first d/(dt)(({x}(t,s))(s+t)) ?

The first d/(dt)(({x}(t,s))(s+t)) is d/(dt)({x}(t,s))(s+t)+1*{x}(t,s)

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\frac{d}{d t} ((x (t, s)) (s + t))

\frac{d}{d t} (x (t, s)) (s + t) + 1 \cdot x (t, s)

Solution steps

\frac{d}{d t} ((x (t, s)) (s + t))

Apply the Product Rule:

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

f = x (t, s), g = s + t

= \frac{d}{d t} (x (t, s)) (s + t) + \frac{d}{d t} (s + t) x (t, s)

\frac{d}{d t} (s + t) = 1

= \frac{d}{d t} (x (t, s)) (s + t) + 1 \cdot x (t, s)

\frac{4}{( x - 1 ) ( x - 3 ) ( x - 4 )}

\frac{e ^{- s}}{( s + 4 ) ( s - 2 ) ( s - 1 )}

(3 x - 2)^{2}

\frac{2 ( s - 6 )}{7}

What is the d/(dt)(({x}(t,s))(s+t)) ?
The d/(dt)(({x}(t,s))(s+t)) is d/(dt)({x}(t,s))(s+t)+1*{x}(t,s)
What is the first d/(dt)(({x}(t,s))(s+t)) ?
The first d/(dt)(({x}(t,s))(s+t)) is d/(dt)({x}(t,s))(s+t)+1*{x}(t,s)