What is the derivative of sqrt(tan(x+y)) ?

The derivative of sqrt(tan(x+y)) is (sec^2(x)+\frac{dy)/(dx)}{2sqrt(tan(x)+y)}

What is the first derivative of sqrt(tan(x+y)) ?

The first derivative of sqrt(tan(x+y)) is (sec^2(x)+\frac{dy)/(dx)}{2sqrt(tan(x)+y)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(tan(x+y)) ?
The derivative of sqrt(tan(x+y)) is (sec^2(x)+\frac{dy)/(dx)}{2sqrt(tan(x)+y)}
What is the first derivative of sqrt(tan(x+y)) ?
The first derivative of sqrt(tan(x+y)) is (sec^2(x)+\frac{dy)/(dx)}{2sqrt(tan(x)+y)}