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Popular >

derivative of cos(2arctan(x))

Solution

derivative of

cos (2 arctan (x))

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Popular Examples

integral of sin(5x+pi/6)

\int sin (5 x + \frac{π}{6}) d x

derivative of 1/2 x^2+8 derivative of

\frac{1}{2} x^{2} + 8

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derivative of (e^x+x)^4 derivative of

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

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

Frequently Asked Questions (FAQ)

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