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Popular >

derivative of (tan(x)^{1/2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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