derivative of x^7sqrt(x^2-9x+9)

解

\frac{d}{d x} (x^{7} x^{2} - 9 x + 9)

\frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}

解答ステップ

\frac{d}{d x} (x^{7} x^{2} - 9 x + 9)

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = x^{2} - 9 x + 9

= \frac{d}{d x} (x^{7}) x^{2} - 9 x + 9 + \frac{d}{d x} (x^{2} - 9 x + 9) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (x^{2} - 9 x + 9) = \frac{2 x - 9}{2 x ^{2} - 9 x + 9}

= 7 x^{6} x^{2} - 9 x + 9 + \frac{2 x - 9}{2 x ^{2} - 9 x + 9} x^{7}

簡素化

7 x^{6} x^{2} - 9 x + 9 + \frac{2 x - 9}{2 x ^{2} - 9 x + 9} x^{7} : \frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}

= \frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}