What is (\partial)/(\partial z)(xarctan(yz)) ?

The answer to (\partial)/(\partial z)(xarctan(yz)) is (xy)/(y^2z^2+1)

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(\partial)/(\partial z)(xarctan(yz))

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (yz) = y

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

Simplify

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

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

\frac{\partial}{\partial x} ((2 x + 3 y)^{2})

x \to 0 lim (\frac{1}{x - 3})

\frac{t}{7}

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

\frac{1}{( s ( s ^{2} + 6 s - 27 ) )}

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