What is (\partial)/(\partial y)((y-2)(2x+y-5)) ?

The answer to (\partial)/(\partial y)((y-2)(2x+y-5)) is 2y+2x-7

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(\partial)/(\partial y)((y-2)(2x+y-5))

\frac{\partial}{\partial y} ((y - 2) (2 x + y - 5))

2 y + 2 x - 7

Solution steps

\frac{\partial}{\partial y} ((y - 2) (2 x + y - 5))

Treat

x

as a constant

Apply the Product Rule:

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

f = y - 2, g = 2 x + y - 5

= \frac{\partial}{\partial y} (y - 2) (2 x + y - 5) + \frac{\partial}{\partial y} (2 x + y - 5) (y - 2)

\frac{\partial}{\partial y} (y - 2) = 1

\frac{\partial}{\partial y} (2 x + y - 5) = 1

= 1 \cdot (2 x + y - 5) + 1 \cdot (y - 2)

Simplify

1 \cdot (2 x + y - 5) + 1 \cdot (y - 2) : 2 y + 2 x - 7

= 2 y + 2 x - 7

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 4 x - y}

\int_{0}^{1} (x^{2} - 3 x + 5) d x

f (x) = \frac{2}{3 x ^{\frac{2}{3}}}, at x = 64

\frac{\partial}{\partial x} (64 - 8 x^{2} - y^{2})

x \to 1 + lim (\frac{1 - x}{x ( x - 1 )})

What is (\partial)/(\partial y)((y-2)(2x+y-5)) ?
The answer to (\partial)/(\partial y)((y-2)(2x+y-5)) is 2y+2x-7