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

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

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

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the Product Rule:

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

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

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

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

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

(7 cos (x) + 1)^{2}

3 π (3 - 2)

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} - z^{2}))

4^{3}

x^{2} - 2 (a + \frac{1}{a}) x + 4

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