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

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

(\partial)/(\partial y)(xarctan(yz))

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

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

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

Simplify

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

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

\int e^{- (x^{2} + 1)} x d x

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x)

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

\frac{\partial}{\partial x} (sin (z^{3}) cos (x y))

\int \frac{x}{( x ^{2} + 4 x + 5 ) ^{2}} d x

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