derivative 2arctan(x/2)

해법

유도체

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

\frac{4}{x ^{2} + 4}

솔루션 단계

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

정수를 빼라:

(a \cdot f)^{'} = a \cdot f^{'}

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

체인 규칙 적용:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

2 \cdot \frac{1}{( \frac{x}{2} ) ^{2} + 1} \cdot \frac{1}{2}

간소화하다 :

\frac{4}{x ^{2} + 4}

= \frac{4}{x ^{2} + 4}