What is the derivative of f(x)=tan(sqrt(x)) ?

The derivative of f(x)=tan(sqrt(x)) is (sec^2(sqrt(x)))/(2sqrt(x))

What is the first derivative of f(x)=tan(sqrt(x)) ?

The first derivative of f(x)=tan(sqrt(x)) is (sec^2(sqrt(x)))/(2sqrt(x))

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derivative of

f (x) = tan (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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