What is the derivative of sqrt(1+tan(x)) ?

The derivative of sqrt(1+tan(x)) is (sec^2(x))/(2sqrt(1+tan(x)))

What is the first derivative of sqrt(1+tan(x)) ?

The first derivative of sqrt(1+tan(x)) is (sec^2(x))/(2sqrt(1+tan(x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(1+tan(x)) ?
The derivative of sqrt(1+tan(x)) is (sec^2(x))/(2sqrt(1+tan(x)))
What is the first derivative of sqrt(1+tan(x)) ?
The first derivative of sqrt(1+tan(x)) is (sec^2(x))/(2sqrt(1+tan(x)))