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Popular >

derivative of (arctan(2x)^2)

Solution

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

Solution

\frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (2 x)) = \frac{2}{4 x ^{2} + 1}

= 2 arctan (2 x) \frac{2}{4 x ^{2} + 1}

Simplify

2 arctan (2 x) \frac{2}{4 x ^{2} + 1} : \frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

= \frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

Popular Examples

integral of ((x-1))/(x^2)

\int \frac{( x - 1 )}{x ^{2}} d x

derivative of x^2sqrt(x)-5x

\frac{d}{d x} (x^{2} x - 5 x)

area y=2-e^x,y=10e^{-x}-5 area

y = 2 - e^{x}, y = 10 e^{- x} - 5

derivative of f(x)=(ln(4))/3 e^x derivative of

f (x) = \frac{ln ( 4 )}{3} e^{x}

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y = \frac{5 x - 2}{x}

Frequently Asked Questions (FAQ)

What is the derivative of (arctan(2x)^2) ?
The derivative of (arctan(2x)^2) is (4arctan(2x))/(4x^2+1)
What is the first derivative of (arctan(2x)^2) ?
The first derivative of (arctan(2x)^2) is (4arctan(2x))/(4x^2+1)