What is the derivative of f(x)=tan(2sqrt(x)) ?

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

What is the first derivative of f(x)=tan(2sqrt(x)) ?

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

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derivative of

f (x) = tan (2 x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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