derivative of (7+8x-4sqrt(x)/x)

해법

\frac{d}{d x} (\frac{7 + 8 x - 4 x}{x})

\frac{2 x - 7}{x ^{2}}

솔루션 단계

\frac{d}{d x} (\frac{7 + 8 x - 4 x}{x})

상수 규칙 적용:

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

= \frac{\frac{d}{d x} ( 7 + 8 x - 4 x ) x - \frac{d x}{d x} ( 7 + 8 x - 4 x )}{x ^{2}}

\frac{d}{d x} (7 + 8 x - 4 x) = - \frac{2}{x} + 8

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

= \frac{( - \frac{2}{x} + 8 ) x - 1 \cdot ( 7 + 8 x - 4 x )}{x ^{2}}

\frac{( - \frac{2}{x} + 8 ) x - 1 \cdot ( 7 + 8 x - 4 x )}{x ^{2}}

간소화하다 :

\frac{2 x - 7}{x ^{2}}

= \frac{2 x - 7}{x ^{2}}