derivative 10sqrt(6x^9+9x^6)

解答

导数

10 6 x^{9} + 9 x^{6}

\frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}

求解步骤

\frac{d}{d x} (10 6 x^{9} + 9 x^{6})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (6 x^{9} + 9 x^{6})

使用连锁律:

\frac{1}{2 6 x ^{9} + 9 x ^{6}} \frac{d}{d x} (6 x^{9} + 9 x^{6})

= \frac{1}{2 6 x ^{9} + 9 x ^{6}} \frac{d}{d x} (6 x^{9} + 9 x^{6})

\frac{d}{d x} (6 x^{9} + 9 x^{6}) = 54 x^{8} + 54 x^{5}

= 10 \cdot \frac{1}{2 6 x ^{9} + 9 x ^{6}} (54 x^{8} + 54 x^{5})

化简

10 \cdot \frac{1}{2 6 x ^{9} + 9 x ^{6}} (54 x^{8} + 54 x^{5}) : \frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}

= \frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}