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

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

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

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

x + 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d y} (x^{2}) = 0

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

\frac{d}{d y} (y^{2}) = 2 y

= 0 + x + 2 y

Simplify

= x + 2 y

\int_{0}^{4} 2 x - x d x

x \to 0 lim (\frac{1}{x ^{3} - 1} + 1)

x \to 0 lim (\frac{x ^{2} - 5}{x})

t \to - 2 lim (t^{2} + 5 t + 7)

\int tan^{3} (\frac{x}{2}) sec^{3} (\frac{x}{2}) d x