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Popular >

derivative of sqrt(tan(4x))

Solution

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

Solution

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)

Popular Examples

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\frac{d y}{d x} + \frac{y}{x - 2} = 5 (x - 2) y^{\frac{1}{2}}

derivative of f(x)=(6x^2-1)/(2sqrt(x))derivative of

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

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derivative of 4x^3-238x^2+3160x

\frac{d}{d x} (4 x^{3} - 238 x^{2} + 3160 x)

Frequently Asked Questions (FAQ)

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))