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

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

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

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

\frac{sec ^{2} ( x )}{2 tan ( x ) + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int cos^{4} (2 y) d y

cos (3 x) y^{^{'}} + 3 (tan (3 x)) y = sec (3 x)

\frac{\partial}{\partial x} (e^{- 2 x} cos (2 π t))

y^{^{'}} = \frac{( 4 - 2 x )}{( 3 + 2 y )}

\frac{3 x}{x ^{2} - 6}

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