(\partial)/(\partial x)(2/(x-3))

الحلّ

\frac{\partial}{\partial x} (\frac{2}{x - 3})

- \frac{2}{( x - 3 ) ^{2}}

خطوات الحلّ

\frac{\partial}{\partial x} (\frac{2}{x - 3})

(a \cdot f)^{'} = a \cdot f^{'}

:استخرج الثابت

= 2 \frac{\partial}{\partial x} (\frac{1}{x - 3})

\frac{1}{a} = a^{- 1}

:فعّل قانون القوى

= 2 \frac{\partial}{\partial x} ((x - 3)^{- 1})

استعمل قانون السلسلة:

- \frac{1}{( x - 3 ) ^{2}} \frac{\partial}{\partial x} (x - 3)

= - \frac{1}{( x - 3 ) ^{2}} \frac{\partial}{\partial x} (x - 3)

\frac{\partial}{\partial x} (x - 3) = 1

= 2 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1)

2 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1)

بسّط:

- \frac{2}{( x - 3 ) ^{2}}

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

2 arcsin (x^{4})

x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

\frac{5 x ^{4}}{e ^{x}}

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

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