derivative y=xln^3(x)

解答

导数

y = x ln^{3} (x)

ln^{3} (x) + 3 ln^{2} (x)

求解步骤

\frac{d}{d x} (x ln^{3} (x))

使用微分乘法定则:

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

f = x, g = ln^{3} (x)

= \frac{d x}{d x} ln^{3} (x) + \frac{d}{d x} (ln^{3} (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln^{3} (x)) = \frac{3 ln ^{2} ( x )}{x}

= 1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x

化简

1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x : ln^{3} (x) + 3 ln^{2} (x)

= ln^{3} (x) + 3 ln^{2} (x)

\frac{\partial}{\partial x} (x - x^{2} y - y + x y^{2})

x \to 0 lim (x^{7} sin (\frac{1}{x}))

d er i v a t i v e (9 - \frac{x}{9})^{- 7}

a re a x = - 2, x = 1, y = 7 x, y = x^{2} - 8

im pl i c i t \frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0