derivative of sqrt((x-y/(x+y)))

الحلّ

\frac{d}{d x} (\frac{x - y}{x + y})

\frac{- x \frac{d y}{d x} + y}{x - y ( x + y ) ^{\frac{3}{2}}}

خطوات الحلّ

\frac{d}{d x} (\frac{x - y}{x + y})

استعمل قانون السلسلة:

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

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

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

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

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

بسّط:

\frac{- x \frac{d y}{d x} + y}{x - y ( x + y ) ^{\frac{3}{2}}}

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

e^{- 0.5 \cdot 10}

x (2 x y e^{x y^{2}})

(2.3 \cdot 1 0^{- 19}) \cdot 0.28

16 e^{- 0.000121 (8967)}