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

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

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(\partial)/(\partial x)(sqrt(x^2y^2))

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

y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= y

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

x \to - 4 - lim (x + 4)

\int sec^{2} (x) d x

\frac{d}{d x} (\frac{x}{1 - ln ( x - 7 )})

x \to - 2 + lim (\frac{x ^{2}}{x + 2})

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