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

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

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

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

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

\frac{2 y ^{2} + x ^{2}}{x ^{2} + y ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = y, g = x^{2} + y^{2}

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

\frac{d y}{d y} = 1

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

= 1 \cdot x^{2} + y^{2} + \frac{y}{x ^{2} + y ^{2}} y

Simplify

1 \cdot x^{2} + y^{2} + \frac{y}{x ^{2} + y ^{2}} y : \frac{2 y ^{2} + x ^{2}}{x ^{2} + y ^{2}}

= \frac{2 y ^{2} + x ^{2}}{x ^{2} + y ^{2}}

k = 0 \sum \infty \frac{x ^{k}}{k !}

- cos (x), cos^{2} (x), [\frac{- π}{2}, \frac{π}{2}]

\int 12 x d x

\int \frac{3}{t} d t

x \to 8 lim (\frac{x}{ln ( 9 - x )})

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