What is the d/(dy)((2-x)(y-2)(3-x-y)) ?

The d/(dy)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)

What is the first d/(dy)((2-x)(y-2)(3-x-y)) ?

The first d/(dy)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)

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\frac{d}{d y} ((2 - x) (y - 2) (3 - x - y))

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

Solution steps

\frac{d}{d y} ((2 - x) (y - 2) (3 - x - y))

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{x + 1}{2 x + 1} d x

\int 5 sin^{2} (x) d x

\frac{d}{d x} (2 x^{2} - 5 x + 4)

100

\int (x - 4)^{2} x^{2} d x

What is the d/(dy)((2-x)(y-2)(3-x-y)) ?
The d/(dy)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)
What is the first d/(dy)((2-x)(y-2)(3-x-y)) ?
The first d/(dy)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)