derivative f(x)=(1+x+x^2)^{99}

解答

导数

f (x) = (1 + x + x^{2})^{99}

99 (1 + x + x^{2})^{98} (2 x + 1)

求解步骤

\frac{d}{d x} ((1 + x + x^{2})^{99})

使用连锁律:

99 (1 + x + x^{2})^{98} \frac{d}{d x} (1 + x + x^{2})

= 99 (1 + x + x^{2})^{98} \frac{d}{d x} (1 + x + x^{2})

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

= 99 (1 + x + x^{2})^{98} (2 x + 1)

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