What is the derivative of cos(arctan(2x)) ?

The derivative of cos(arctan(2x)) is -(4x)/((4x^2+1)sqrt(1+4x^2))

What is the first derivative of cos(arctan(2x)) ?

The first derivative of cos(arctan(2x)) is -(4x)/((4x^2+1)sqrt(1+4x^2))

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derivative of

cos (arctan (2 x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (z x)

\frac{d}{d t} (sin (t) (1 - sin (t)))

\frac{d y}{d x} + 2 = x

x \to 0 lim (+ sin (x) ln (x))

x \to 0 lim (x^{2} cos (\frac{1}{2}))

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