What is the derivative of sqrt(tan(4x)) ?

The derivative of sqrt(tan(4x)) is 2sec^2(4x)sqrt(cot(4x))

What is the first derivative of sqrt(tan(4x)) ?

The first derivative of sqrt(tan(4x)) is 2sec^2(4x)sqrt(cot(4x))

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\frac{d}{d x} (tan (4 x))

2 sec^{2} (4 x) cot (4 x)

Solution steps

\frac{d}{d x} (tan (4 x))

Apply the chain rule:

\frac{1}{2 tan ( 4 x )} \frac{d}{d x} (tan (4 x))

= \frac{1}{2 tan ( 4 x )} \frac{d}{d x} (tan (4 x))

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

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

Simplify

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

= 2 sec^{2} (4 x) cot (4 x)

What is the derivative of sqrt(tan(4x)) ?
The derivative of sqrt(tan(4x)) is 2sec^2(4x)sqrt(cot(4x))
What is the first derivative of sqrt(tan(4x)) ?
The first derivative of sqrt(tan(4x)) is 2sec^2(4x)sqrt(cot(4x))