What is (\partial)/(\partial x)(-(x-2)(y-2)(x+y-3)) ?

The answer to (\partial)/(\partial x)(-(x-2)(y-2)(x+y-3)) is -(y-2)(2x+y-5)

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(\partial)/(\partial x)(-(x-2)(y-2)(x+y-3))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{\partial}{\partial x} (x + y - 3) = 1

= - (y - 2) (1 \cdot (x + y - 3) + 1 \cdot (x - 2))

Simplify

- (y - 2) (1 \cdot (x + y - 3) + 1 \cdot (x - 2)) : - (y - 2) (2 x + y - 5)

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

\int \frac{4 x}{3 x ^{2} - 1} d x

\frac{\partial}{\partial x} (e^{- 4 x})

x \to \frac{π}{2} lim (4 sec (x))

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

What is (\partial)/(\partial x)(-(x-2)(y-2)(x+y-3)) ?
The answer to (\partial)/(\partial x)(-(x-2)(y-2)(x+y-3)) is -(y-2)(2x+y-5)