derivative y=\sqrt[3]{1.6x^2+4.9}

解答

导数

y = 3 1.6 x^{2} + 4.9

\frac{1.06666 \dots x}{( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (3 1.6 x^{2} + 4.9)

使用连锁律:

\frac{1}{3 ( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}} \frac{d}{d x} (1.6 x^{2} + 4.9)

= \frac{1}{3 ( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}} \frac{d}{d x} (1.6 x^{2} + 4.9)

\frac{d}{d x} (1.6 x^{2} + 4.9) = 3.2 x

= \frac{1}{3 ( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}} \cdot 3.2 x

化简

\frac{1}{3 ( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}} \cdot 3.2 x : \frac{1.06666 \dots x}{( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}}

= \frac{1.06666 \dots x}{( 1.6 x ^{2} + 4.9 ) ^{\frac{2}{3}}}

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