What is (\partial)/(\partial z)(xy^2arctan(z)) ?

The answer to (\partial)/(\partial z)(xy^2arctan(z)) is (xy^2)/(z^2+1)

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(\partial)/(\partial z)(xy^2arctan(z))

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial z} (arctan (z)) = \frac{1}{z ^{2} + 1}

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

Simplify

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

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

\int_{1}^{2} \frac{3}{x ^{2}} d x

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

f (t) = - 16 t^{2} + 32 t + 240, at t = 240

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

\frac{\partial}{\partial x} (\frac{90}{6 + x ^{2} + y ^{2}})

What is (\partial)/(\partial z)(xy^2arctan(z)) ?
The answer to (\partial)/(\partial z)(xy^2arctan(z)) is (xy^2)/(z^2+1)