$$$\sqrt{x} \ln\left(2\right)$$$의 도함수
사용자 입력
$$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right)$$$을(를) 구하시오.
풀이
상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = \ln\left(2\right)$$$와 $$$f{\left(x \right)} = \sqrt{x}$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right)\right)} = {\color{red}\left(\ln\left(2\right) \frac{d}{dx} \left(\sqrt{x}\right)\right)}$$거듭제곱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = \frac{1}{2}$$$에 적용합니다:
$$\ln\left(2\right) {\color{red}\left(\frac{d}{dx} \left(\sqrt{x}\right)\right)} = \ln\left(2\right) {\color{red}\left(\frac{1}{2 \sqrt{x}}\right)}$$따라서, $$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right) = \frac{\ln\left(2\right)}{2 \sqrt{x}}$$$.
정답
$$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right) = \frac{\ln\left(2\right)}{2 \sqrt{x}}$$$A