derivative y=(x^2+x+1)/x

해법

유도체

y = \frac{x ^{2} + x + 1}{x}

\frac{x ^{2} - 1}{x ^{2}}

솔루션 단계

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

상수 규칙 적용:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

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

간소화하다 :

\frac{x ^{2} - 1}{x ^{2}}

= \frac{x ^{2} - 1}{x ^{2}}