derivative y=ln(sqrt(5x)*(2x^3-4x)^5)

解答

导数

y = ln (5 x \cdot (2 x^{3} - 4 x)^{5})

\frac{31 x ^{2} - 22}{2 x ( x ^{2} - 2 )}

求解步骤

\frac{d}{d x} (ln (5 x (2 x^{3} - 4 x)^{5}))

化简

ln (5 x (2 x^{3} - 4 x)^{5}) : ln (x (2 x^{3} - 4 x)^{5}) + \frac{1}{2} ln (5)

= \frac{d}{d x} (ln (x (2 x^{3} - 4 x)^{5}) + \frac{1}{2} ln (5))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x (2 x^{3} - 4 x)^{5})) + \frac{d}{d x} (\frac{1}{2} ln (5))

\frac{d}{d x} (ln (x (2 x^{3} - 4 x)^{5})) = \frac{31 x ^{2} - 22}{2 x ( x ^{2} - 2 )}

\frac{d}{d x} (\frac{1}{2} ln (5)) = 0

= \frac{31 x ^{2} - 22}{2 x ( x ^{2} - 2 )} + 0

化简

= \frac{31 x ^{2} - 22}{2 x ( x ^{2} - 2 )}