展開する (derivative of 5)/(4(3x^2+6x^4+2)^3)

解

展開する

\frac{\frac{d}{d x} ( 5 )}{4 ( 3 x ^{2} + 6 x ^{4} + 2 ) ^{3}}

\frac{\frac{d}{d x} ( 5 )}{864 x ^{12} + 1296 x ^{10} + 1512 x ^{8} + 972 x ^{6} + 504 x ^{4} + 144 x ^{2} + 32}

解答ステップ

\frac{\frac{d}{d x} ( 5 )}{4 ( 3 x ^{2} + 6 x ^{4} + 2 ) ^{3}}

(3 x^{2} + 6 x^{4} + 2)^{3} = 216 x^{12} + 324 x^{10} + 378 x^{8} + 243 x^{6} + 126 x^{4} + 36 x^{2} + 8

= \frac{\frac{d}{d x} ( 5 )}{4 ( 216 x ^{12} + 324 x ^{10} + 378 x ^{8} + 243 x ^{6} + 126 x ^{4} + 36 x ^{2} + 8 )}

拡張

4 (216 x^{12} + 324 x^{10} + 378 x^{8} + 243 x^{6} + 126 x^{4} + 36 x^{2} + 8) : 864 x^{12} + 1296 x^{10} + 1512 x^{8} + 972 x^{6} + 504 x^{4} + 144 x^{2} + 32

= \frac{\frac{d}{d x} ( 5 )}{864 x ^{12} + 1296 x ^{10} + 1512 x ^{8} + 972 x ^{6} + 504 x ^{4} + 144 x ^{2} + 32}