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

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

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(\partial)/(\partial x)(zarctan(yx))

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

Simplify

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

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

\int \frac{1}{4 e ^{- 3 x} + e ^{3 x}} d x

\int_{- 2}^{1} (x - 6 ∣ x ∣) d x

x \to 0 lim (- x^{4})

y^{^{''}} + 4 y = x - \frac{x ^{2}}{20}

\frac{d}{d x} (ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}}))

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