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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

\int \frac{u ^{2}}{u ^{2} - 8 u} d u

\frac{d}{d x} (x^{\frac{1}{3}} (x + 4))

\frac{2}{1 + 3 x + x ^{2}}

(24 + x^{2}) y^{^{'}} - 2 x y = 0

\frac{d y}{d x} = \frac{y ^{3}}{x}, y (1) = 1

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