What is (\partial)/(\partial x)((u(x,y))(x+y)) ?

The answer to (\partial)/(\partial x)((u(x,y))(x+y)) is u((,y*1)(x+y)+1*(x,y))

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(\partial)/(\partial x)((u(x,y))(x+y))

\frac{\partial}{\partial x} ((u (x, y)) (x + y))

u ((, y \cdot 1) (x + y) + 1 \cdot (x, y))

Solution steps

\frac{\partial}{\partial x} ((u (x, y)) (x + y))

Treat

u, y

as constants

Take the constant out:

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

= u \frac{\partial}{\partial x} ((x, y) (x + y))

Apply the Product Rule:

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

f = x, y, g = x + y

= u (\frac{\partial}{\partial x} (x, y) (x + y) + \frac{\partial}{\partial x} (x + y) (x, y))

\frac{\partial}{\partial x} (x, y) = (, y \cdot 1)

\frac{\partial}{\partial x} (x + y) = 1

= u ((, y \cdot 1) (x + y) + 1 \cdot (x, y))

(1 - x^{\frac{1}{2}})^{3}

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

(x^{\frac{1}{3}} - \frac{1}{4} x^{- \frac{1}{3}})^{2}

tan (h) (x - y)

(x + ln (x))^{2}

What is (\partial)/(\partial x)((u(x,y))(x+y)) ?
The answer to (\partial)/(\partial x)((u(x,y))(x+y)) is u((,y*1)(x+y)+1*(x,y))