What is (\partial)/(\partial x)(sqrt(x^2+8xy+3y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+8xy+3y^2)) is (x+4y)/(sqrt(x^2+8xy+3y^2))

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(\partial)/(\partial x)(sqrt(x^2+8xy+3y^2))

\frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2})

\frac{x + 4 y}{x ^{2} + 8 x y + 3 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + 8 x y + 3 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2})

= \frac{1}{2 x ^{2} + 8 x y + 3 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2})

\frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2}) = 2 x + 8 y

= \frac{1}{2 x ^{2} + 8 x y + 3 y ^{2}} (2 x + 8 y)

Simplify

\frac{1}{2 x ^{2} + 8 x y + 3 y ^{2}} (2 x + 8 y) : \frac{x + 4 y}{x ^{2} + 8 x y + 3 y ^{2}}

= \frac{x + 4 y}{x ^{2} + 8 x y + 3 y ^{2}}

\frac{x ^{2}}{x - 5}

n \to \infty lim (n + 1)

\int \frac{x ^{2}}{x ^{2} + 3} d x

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

\int e^{- x} \cdot sin (x) d x

What is (\partial)/(\partial x)(sqrt(x^2+8xy+3y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+8xy+3y^2)) is (x+4y)/(sqrt(x^2+8xy+3y^2))