derivative of 3sqrt(x)-4x^3+2^x-e+7

解答

\frac{d}{d x} (3 x - 4 x^{3} + 2^{x} - e + 7)

- 12 x^{2} + ln (2) \cdot 2^{x} + \frac{3}{2 x}

求解步骤

\frac{d}{d x} (3 x - 4 x^{3} + 2^{x} - e + 7)

使用微分加减法定则:

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

= \frac{d}{d x} (3 x) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (2^{x}) - \frac{d e}{d x} + \frac{d}{d x} (7)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

\frac{d e}{d x} = 0

\frac{d}{d x} (7) = 0

= \frac{3}{2 x} - 12 x^{2} + 2^{x} ln (2) - 0 + 0

化简

= - 12 x^{2} + ln (2) \cdot 2^{x} + \frac{3}{2 x}

t an g e n t y = 1 + x^{3}, (2, 3)

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