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

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

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

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

2 x + 2 y - 7

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 2 x + 2 y - 7

x \to 2 lim (\frac{3 x + 4}{5 x + 7})

\frac{d}{d x} (\frac{1}{cos ( x )} + \frac{1}{sin ( x + 1 )})

\frac{d}{d θ} (\frac{e ^{i θ} + e ^{- i θ}}{2})

y = \frac{t - t}{t ^{\frac{1}{3}}}

\int \frac{4 x + 5}{x ^{2} + 1} d x

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