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

The answer to (\partial)/(\partial y)(xy^2arctan(z)) is 2xyarctan(z)

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

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

2 x y arctan (z)

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x arctan (z) \cdot 2 y^{2 - 1}

Simplify

= 2 x y arctan (z)

(4 x + 2 y) d x + (2 x + 2 y) d y = 0

x^{2} + y^{2} = 1, y = 1 - x

n = 1 \sum \infty \frac{3}{n ^{3}}

y = \frac{9}{x - 2}, (3, 9)

\int_{- 2}^{2} (- x^{2} + 4) d x

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