What is (\partial)/(\partial x)((u(x,y))(2x+3xy)) ?

The answer to (\partial)/(\partial x)((u(x,y))(2x+3xy)) is u((,y*1)(2x+3xy)+(2+3y)(x,y))

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(\partial)/(\partial x)((u(x,y))(2x+3xy))

\frac{\partial}{\partial x} ((u (x, y)) (2 x + 3 x y))

u ((, y \cdot 1) (2 x + 3 x y) + (2 + 3 y) (x, y))

Solution steps

\frac{\partial}{\partial x} ((u (x, y)) (2 x + 3 x y))

Treat

u, y

as constants

Take the constant out:

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

= u \frac{\partial}{\partial x} ((x, y) (2 x + 3 x y))

Apply the Product Rule:

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

f = x, y, g = 2 x + 3 x y

= u (\frac{\partial}{\partial x} (x, y) (2 x + 3 x y) + \frac{\partial}{\partial x} (2 x + 3 x y) (x, y))

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

\frac{\partial}{\partial x} (2 x + 3 x y) = 2 + 3 y

= u ((, y \cdot 1) (2 x + 3 x y) + (2 + 3 y) (x, y))

\frac{\partial}{\partial x} ((y) (y + sin (y) - x))

\frac{2 e ^{- 3 s}}{s ^{2} ( s - 1 ) ( s - 2 )}

(B + BC) (B + B^{^{'}} C) (B + C)

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

e^{x} (1 + e^{x})^{10}

What is (\partial)/(\partial x)((u(x,y))(2x+3xy)) ?
The answer to (\partial)/(\partial x)((u(x,y))(2x+3xy)) is u((,y*1)(2x+3xy)+(2+3y)(x,y))