What is (\partial)/(\partial x)(arctan(yx)) ?

The answer to (\partial)/(\partial x)(arctan(yx)) is y/(y^2x^2+1)

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(\partial)/(\partial x)(arctan(yx))

\frac{\partial}{\partial x} (arctan (y x))

\frac{y}{y ^{2} x ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (arctan (y x))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (1 + x)

x y^{^{'}} - y = x^{2}

x \to 7 lim (x - 7)

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

\frac{d}{d x} (\frac{x ^{2} + sec ( x )}{x - 2 e ^{x}})

What is (\partial)/(\partial x)(arctan(yx)) ?
The answer to (\partial)/(\partial x)(arctan(yx)) is y/(y^2x^2+1)