derivative of 3/4 x^2-5x^3

解答

\frac{d}{d x} (\frac{3}{4} x^{2} - 5 x^{3})

\frac{3 x}{2} - 15 x^{2}

求解步骤

\frac{d}{d x} (\frac{3}{4} x^{2} - 5 x^{3})

化简

\frac{3}{4} x^{2} - 5 x^{3} : \frac{3 x ^{2}}{4} - 5 x^{3}

= \frac{d}{d x} (\frac{3 x ^{2}}{4} - 5 x^{3})

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{3 x ^{2}}{4}) - \frac{d}{d x} (5 x^{3})

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

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

= \frac{3 x}{2} - 15 x^{2}

\int \frac{1}{- 2 x} d x

l a pl a ce t r an s f or m cos^{2} (25 t)

d er i v a t i v e 5 x - 2 x

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\int sin (4 x - 2) d x