derivative of ln({g}(x(3x^2)))

解答

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

\frac{x \frac{d}{d x} ( g ( x ) ) + 2 g ( x )}{x g ( x )}

求解步骤

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

使用连锁律:

\frac{1}{g ( x ) \cdot 3 x ^{2}} \frac{d}{d x} (g (x) \cdot 3 x^{2})

= \frac{1}{g ( x ) \cdot 3 x ^{2}} \frac{d}{d x} (g (x) \cdot 3 x^{2})

\frac{d}{d x} (g (x) \cdot 3 x^{2}) = 3 (\frac{d}{d x} (g (x)) x^{2} + 2 x g (x))

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

化简

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

= \frac{x \frac{d}{d x} ( g ( x ) ) + 2 g ( x )}{x g ( x )}

\frac{d}{d x} (e^{2 x} sin (x))

\int \frac{y}{( y + 5 ) ( 2 y - 1 )} d y

t a y l or f (t) = ln (1 + 2 \cdot t)

\int \frac{7}{( x - 10 ) ^{7}} d x

\int \frac{x}{3 x - 2} d x