What is (\partial)/(\partial x)(sqrt(x^2+6xy+9y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+6xy+9y^2)) is 1

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(\partial)/(\partial x)(sqrt(x^2+6xy+9y^2))

\frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2})

1

Solution steps

\frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + 6 x y + 9 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2})

= \frac{1}{2 x ^{2} + 6 x y + 9 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2})

\frac{\partial}{\partial x} (x^{2} + 6 x y + 9 y^{2}) = 2 x + 6 y

= \frac{1}{2 x ^{2} + 6 x y + 9 y ^{2}} (2 x + 6 y)

Simplify

\frac{1}{2 x ^{2} + 6 x y + 9 y ^{2}} (2 x + 6 y) : 1

= 1

\frac{d}{d x} (ln (2 x))

\int cos (x) (2 + 5 sin^{2} (x)) d x

\frac{\partial}{\partial x} (x^{4} ln (zy))

\frac{d}{d x} (\frac{e ^{x}}{x ^{n}})

\frac{d}{d x} (3 1 - 2 x)

What is (\partial)/(\partial x)(sqrt(x^2+6xy+9y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+6xy+9y^2)) is 1