derivative of yln(x)

解答

\frac{d}{d x} (y ln (x))

ln (x) \frac{d y}{d x} + \frac{y}{x}

求解步骤

\frac{d}{d x} (y ln (x))

使用微分乘法定则:

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

f = y, g = ln (x)

= \frac{d y}{d x} ln (x) + \frac{d}{d x} (ln (x)) y

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= \frac{d y}{d x} ln (x) + \frac{1}{x} y

\frac{1}{x} y = \frac{y}{x}

= ln (x) \frac{d y}{d x} + \frac{y}{x}

t an g e n t 6 cos (t), at t = - \frac{π}{4}

in v erse l a pl a ce 2 s + 1

t an g e n t f (x) = x^{4} - 4 x^{3} + 2 x^{2} - 6, at x = 1

\int \frac{x ^{2}}{x ^{2} + x + 12} d x

x y \frac{d y}{d x} = 7