What is (\partial)/(\partial y)(arctan(yz)) ?

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

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(\partial)/(\partial y)(arctan(yz))

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

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

Solution steps

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

Treat

z

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

e^{- x} (y^{^{'}} - y) = y^{2}

x \to \infty lim (\frac{ln ( 1 + e ^{- x} )}{e ^{- x}})

x \to - 1 lim (3 (2 x - 1)^{2})

\int \frac{3 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

- \frac{5}{x ^{6}}

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