What is (\partial)/(\partial y)(sqrt(tan(x)+y)) ?

The answer to (\partial)/(\partial y)(sqrt(tan(x)+y)) is 1/(2sqrt(tan(x)+y))

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(\partial)/(\partial y)(sqrt(tan(x)+y))

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

\frac{1}{2 tan ( x ) + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 tan ( x ) + y} \frac{\partial}{\partial y} (tan (x) + y)

= \frac{1}{2 tan ( x ) + y} \frac{\partial}{\partial y} (tan (x) + y)

\frac{\partial}{\partial y} (tan (x) + y) = 1

= \frac{1}{2 tan ( x ) + y} \cdot 1

Simplify

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

What is (\partial)/(\partial y)(sqrt(tan(x)+y)) ?
The answer to (\partial)/(\partial y)(sqrt(tan(x)+y)) is 1/(2sqrt(tan(x)+y))