derivative ln(x^4+2)

解答

导数

ln (x^{4} + 2)

\frac{4 x ^{3}}{x ^{4} + 2}

求解步骤

\frac{d}{d x} (ln (x^{4} + 2))

使用连锁律:

\frac{1}{x ^{4} + 2} \frac{d}{d x} (x^{4} + 2)

= \frac{1}{x ^{4} + 2} \frac{d}{d x} (x^{4} + 2)

\frac{d}{d x} (x^{4} + 2) = 4 x^{3}

= \frac{1}{x ^{4} + 2} \cdot 4 x^{3}

化简

\frac{1}{x ^{4} + 2} \cdot 4 x^{3} : \frac{4 x ^{3}}{x ^{4} + 2}

= \frac{4 x ^{3}}{x ^{4} + 2}

\frac{d y}{d x} = 2 y - x

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

x \to 0 lim (\frac{x ^{2} ln ( x )}{x})

\frac{\partial}{\partial x} ((y - 2) (arctan (x)))

\frac{d}{d x} (\frac{csc ( x )}{2 ^{x}})