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Popular >

derivative of y=(arctan(2x))^2

Solution

derivative of

y = (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

derivative of arctan(sqrt(x^3))

\frac{d}{d x} (arctan (x^{3}))

derivative of arcsin(5x^2)

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

(\partial)/(\partial x)(x^2y-1)

\frac{\partial}{\partial x} (x^{2} y - 1)

y^'=(2y+1)cot(x)

y^{^{'}} = (2 y + 1) cot (x)

derivative of (3x^2/(x^2+1))

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

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