derivative ln((8-x)/(8+x))

الحلّ

derivative of

ln (\frac{8 - x}{8 + x})

- \frac{16}{( - x + 8 ) ( x + 8 )}

خطوات الحلّ

\frac{d}{d x} (ln (\frac{8 - x}{8 + x}))

استعمل قانون السلسلة:

\frac{1}{\frac{8 - x}{8 + x}} \frac{d}{d x} (\frac{8 - x}{8 + x})

= \frac{1}{\frac{8 - x}{8 + x}} \frac{d}{d x} (\frac{8 - x}{8 + x})

\frac{d}{d x} (\frac{8 - x}{8 + x}) = - \frac{16}{( 8 + x ) ^{2}}

= \frac{1}{\frac{8 - x}{8 + x}} (- \frac{16}{( 8 + x ) ^{2}})

\frac{1}{\frac{8 - x}{8 + x}} (- \frac{16}{( 8 + x ) ^{2}})

بسّط:

- \frac{16}{( - x + 8 ) ( x + 8 )}

= - \frac{16}{( - x + 8 ) ( x + 8 )}

72 x - \frac{4 x ^{3}}{3}

\frac{\partial}{\partial y} (\frac{y}{1 + x ^{2}})

\int \frac{1}{x + 2} d x

\frac{d}{d θ} (2 cos (θ))

\frac{d y}{d x} = (4 x^{2} + 3 x + 2) (y + 5)