|
|
|
|
|
|
|
|
|
|
|
|
$$$x^{4} - 6 x^{2}$$$의 도함수
사용자 입력
$$$\frac{d}{dx} \left(x^{4} - 6 x^{2}\right)$$$을(를) 구하시오.
풀이
합/차의 도함수는 도함수들의 합/차이다:
$${\color{red}\left(\frac{d}{dx} \left(x^{4} - 6 x^{2}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{4}\right) - \frac{d}{dx} \left(6 x^{2}\right)\right)}$$거듭제곱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = 4$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(x^{4}\right)\right)} - \frac{d}{dx} \left(6 x^{2}\right) = {\color{red}\left(4 x^{3}\right)} - \frac{d}{dx} \left(6 x^{2}\right)$$상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = 6$$$와 $$$f{\left(x \right)} = x^{2}$$$에 적용합니다:
$$4 x^{3} - {\color{red}\left(\frac{d}{dx} \left(6 x^{2}\right)\right)} = 4 x^{3} - {\color{red}\left(6 \frac{d}{dx} \left(x^{2}\right)\right)}$$거듭제곱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = 2$$$에 적용합니다:
$$4 x^{3} - 6 {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = 4 x^{3} - 6 {\color{red}\left(2 x\right)}$$간단히 하시오:
$$4 x^{3} - 12 x = 4 x \left(x^{2} - 3\right)$$따라서, $$$\frac{d}{dx} \left(x^{4} - 6 x^{2}\right) = 4 x \left(x^{2} - 3\right)$$$.
정답
$$$\frac{d}{dx} \left(x^{4} - 6 x^{2}\right) = 4 x \left(x^{2} - 3\right)$$$A
Please try a new game Rotatly