derivative of ln((x+b/x))

解答

\frac{d}{d x} (ln (\frac{x + b}{x}))

- \frac{b}{x ( x + b )}

求解步骤

\frac{d}{d x} (ln (\frac{x + b}{x}))

使用连锁律:

\frac{1}{\frac{x + b}{x}} \frac{d}{d x} (\frac{x + b}{x})

= \frac{1}{\frac{x + b}{x}} \frac{d}{d x} (\frac{x + b}{x})

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

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

化简

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

= - \frac{b}{x ( x + b )}

y^{^{'}} + 8 y = 5

\int \frac{3 x ^{4} + 4}{x ^{2} ( x ^{2} + 1 ) ^{3}} d x

a re a y = x^{2}, x = 0, x = 4

\int \frac{( ( x + 1 ) )}{( x ^{2} - x - 6 )} d x

\frac{\partial}{\partial x} (5^{x^{2}})