What is (\partial)/(\partial x)(sqrt(x^2+2xy+y^4)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+2xy+y^4)) is (x+y)/(sqrt(x^2+2xy+y^4))

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(\partial)/(\partial x)(sqrt(x^2+2xy+y^4))

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

\frac{x + y}{x ^{2} + 2 x y + y ^{4}}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + 2 x y + y ^{4}} \frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

= \frac{1}{2 x ^{2} + 2 x y + y ^{4}} \frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4}) = 2 x + 2 y

= \frac{1}{2 x ^{2} + 2 x y + y ^{4}} (2 x + 2 y)

Simplify

\frac{1}{2 x ^{2} + 2 x y + y ^{4}} (2 x + 2 y) : \frac{x + y}{x ^{2} + 2 x y + y ^{4}}

= \frac{x + y}{x ^{2} + 2 x y + y ^{4}}

f (x) = \frac{4}{x}, (- 9, - \frac{4}{9})

\frac{\partial}{\partial y} (x + y - 8)

\frac{\partial}{\partial x} (e^{x^{2}} + 2 y^{3})

\int (x + 1) ln (x) d x

What is (\partial)/(\partial x)(sqrt(x^2+2xy+y^4)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+2xy+y^4)) is (x+y)/(sqrt(x^2+2xy+y^4))