derivative f(x)=(1+3x^4)^2+3x^3

解答

导数

f (x) = (1 + 3 x^{4})^{2} + 3 x^{3}

24 x^{3} (1 + 3 x^{4}) + 9 x^{2}

求解步骤

\frac{d}{d x} ((1 + 3 x^{4})^{2} + 3 x^{3})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((1 + 3 x^{4})^{2}) + \frac{d}{d x} (3 x^{3})

\frac{d}{d x} ((1 + 3 x^{4})^{2}) = 24 x^{3} (1 + 3 x^{4})

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

= 24 x^{3} (1 + 3 x^{4}) + 9 x^{2}

y^{^{''}} + y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

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