What is the first d/(dy)((x+y)^2) ?

The first d/(dy)((x+y)^2) is 2(x+y)

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d/(dy)((x+y)^2)

\frac{d}{d y} ((x + y)^{2})

2 (x + y)

Solution steps

\frac{d}{d y} ((x + y)^{2})

Treat

x

as a constant

Apply the chain rule:

2 (x + y) \frac{d}{d y} (x + y)

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

\frac{d}{d y} (x + y) = 1

= 2 (x + y) \cdot 1

Simplify

= 2 (x + y)

\frac{x ^{2}}{x ^{2} - 1}

x \to 0 lim (\frac{6}{x ^{2}})

cos (θ) - θ sin (θ)

\frac{d}{d x} (\frac{a x + b}{c x - a})

x^{2} - 3, y = 1