What is (\partial)/(\partial y)(xtan(y+z)) ?

The answer to (\partial)/(\partial y)(xtan(y+z)) is xsec^2(y+z)

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(\partial)/(\partial y)(xtan(y+z))

\frac{\partial}{\partial y} (x tan (y + z))

x sec^{2} (y + z)

Solution steps

\frac{\partial}{\partial y} (x tan (y + z))

Treat

x, z

as constants

Take the constant out:

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

= x \frac{\partial}{\partial y} (tan (y + z))

Apply the chain rule:

sec^{2} (y + z) \frac{\partial}{\partial y} (y + z)

= sec^{2} (y + z) \frac{\partial}{\partial y} (y + z)

\frac{\partial}{\partial y} (y + z) = 1

= x sec^{2} (y + z) \cdot 1

Simplify

= x sec^{2} (y + z)

What is (\partial)/(\partial y)(xtan(y+z)) ?
The answer to (\partial)/(\partial y)(xtan(y+z)) is xsec^2(y+z)