derivative f(x)=sqrt(8x^{10)+6x^6}

解

導関数

f (x) = 8 x^{10} + 6 x^{6}

\frac{2 x ^{5} ( 20 x ^{4} + 9 )}{x ^{6} 4 x ^{4} + 3}

解答ステップ

\frac{d}{d x} (8 x^{10} + 6 x^{6})

連鎖法則を適用:

\frac{1}{2 8 x ^{10} + 6 x ^{6}} \frac{d}{d x} (8 x^{10} + 6 x^{6})

= \frac{1}{2 8 x ^{10} + 6 x ^{6}} \frac{d}{d x} (8 x^{10} + 6 x^{6})

\frac{d}{d x} (8 x^{10} + 6 x^{6}) = 80 x^{9} + 36 x^{5}

= \frac{1}{2 8 x ^{10} + 6 x ^{6}} (80 x^{9} + 36 x^{5})

簡素化

\frac{1}{2 8 x ^{10} + 6 x ^{6}} (80 x^{9} + 36 x^{5}) : \frac{2 x ^{5} ( 20 x ^{4} + 9 )}{x ^{6} 4 x ^{4} + 3}

= \frac{2 x ^{5} ( 20 x ^{4} + 9 )}{x ^{6} 4 x ^{4} + 3}