derivative of log_{3}((x^2+2x^4))

解答

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

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

求解步骤

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

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用连锁律:

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

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

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

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

化简

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

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

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

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 4 y = x e^{x}

d er i v a t i v e sin (x) + \frac{3}{5} cot (x)

in v erse l a pl a ce \frac{1}{s + 6}

\frac{\partial}{\partial y} (\frac{y}{x + y + z})