derivative f(x)=sqrt(x^2-x-2)

الحلّ

derivative of

f (x) = x^{2} - x - 2

\frac{2 x - 1}{2 x ^{2} - x - 2}

خطوات الحلّ

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

استعمل قانون السلسلة:

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

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

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

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

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

بسّط:

\frac{2 x - 1}{2 x ^{2} - x - 2}

= \frac{2 x - 1}{2 x ^{2} - x - 2}

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