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Popular >

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

Solution

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

Solution

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

derivative of 2190*e^{-0.3x}

\frac{d}{d x} (2190 \cdot e^{- 0.3 x})

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x \to \frac{π}{2} + lim (3 e^{t a n (x)})

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

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

integral of 15sin^3(xco)s^2x

\int 15 sin^{3} (x co) s^{2} x d x

Frequently Asked Questions (FAQ)

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