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derivative y= x/(x^2+1)

الحلّ

derivative of

y = \frac{x}{x ^{2} + 1}

الحلّ

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

خطوات الحلّ

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

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

:استعمل قانون القسمة

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

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

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

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

1 \cdot (x^{2} + 1) - 2 xx = - x^{2} + 1

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

أمثلة شائعة

slope y=5 slope

y = 5

derivative 3sqrt(x)derivative of

3 x

cartesian (4,-(7pi)/6)polar to cartesian

(4, - \frac{7 π}{6})

slope (1,18),(-8,12)slope

(1, 18), (- 8, 12)

θ = \frac{3 π}{4}