derivative f(x)=-12x^{3/2}+7x^{1.7}+x

解答

导数

f (x) = - 12 x^{\frac{3}{2}} + 7 x^{1.7} + x

- 18 x^{\frac{1}{2}} + 11.9 x^{0.7} + 1

求解步骤

\frac{d}{d x} (- 12 x^{\frac{3}{2}} + 7 x^{1.7} + x)

使用微分加减法定则:

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

= - \frac{d}{d x} (12 x^{\frac{3}{2}}) + \frac{d}{d x} (7 x^{1.7}) + \frac{d x}{d x}

\frac{d}{d x} (12 x^{\frac{3}{2}}) = 18 x^{\frac{1}{2}}

\frac{d}{d x} (7 x^{1.7}) = 11.9 x^{0.7}

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

= - 18 x^{\frac{1}{2}} + 11.9 x^{0.7} + 1

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