What is the derivative of sqrt(tan(\sqrt{x)}) ?

The derivative of sqrt(tan(\sqrt{x)}) is (sec^2(sqrt(x)))/(4sqrt(x)\sqrt{tan(\sqrt{x))}}

What is the first derivative of sqrt(tan(\sqrt{x)}) ?

The first derivative of sqrt(tan(\sqrt{x)}) is (sec^2(sqrt(x)))/(4sqrt(x)\sqrt{tan(\sqrt{x))}}

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

\frac{sec ^{2} ( x )}{4 x tan ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 tan ( x )} \cdot \frac{sec ^{2} ( x )}{2 x} : \frac{sec ^{2} ( x )}{4 x tan ( x )}

= \frac{sec ^{2} ( x )}{4 x tan ( x )}

x \to - \infty lim (1)

\frac{d y}{d t} = y (5 - t y)

x \to 8 lim (\frac{( x - 2 )}{x - 8})

h \to 0 lim (\frac{f ( h ) ( h + 2 ) - 11}{h})

What is the derivative of sqrt(tan(\sqrt{x)}) ?
The derivative of sqrt(tan(\sqrt{x)}) is (sec^2(sqrt(x)))/(4sqrt(x)\sqrt{tan(\sqrt{x))}}
What is the first derivative of sqrt(tan(\sqrt{x)}) ?
The first derivative of sqrt(tan(\sqrt{x)}) is (sec^2(sqrt(x)))/(4sqrt(x)\sqrt{tan(\sqrt{x))}}