derivative of ((12x^4+e^x/(ln(x^4)))^2)

解答

\frac{d}{d x} ((\frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )})^{2})

\frac{( 12 x ^{4} + e ^{x} ) ( 48 x ^{4} ln ( x ) - 12 x ^{4} + e ^{x} x ln ( x ) - e ^{x} )}{8 x ln ^{3} ( x )}

求解步骤

\frac{d}{d x} ((\frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )})^{2})

使用连锁律:

2 \cdot \frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )} \frac{d}{d x} (\frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )})

= 2 \cdot \frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )} \frac{d}{d x} (\frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )})

\frac{d}{d x} (\frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )}) = \frac{x ln ( x ^{4} ) ( 48 x ^{3} + e ^{x} ) - 4 ( 12 x ^{4} + e ^{x} )}{x ln ^{2} ( x ^{4} )}

= 2 \cdot \frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )} \cdot \frac{x ln ( x ^{4} ) ( 48 x ^{3} + e ^{x} ) - 4 ( 12 x ^{4} + e ^{x} )}{x ln ^{2} ( x ^{4} )}

化简

2 \cdot \frac{12 x ^{4} + e ^{x}}{ln ( x ^{4} )} \cdot \frac{x ln ( x ^{4} ) ( 48 x ^{3} + e ^{x} ) - 4 ( 12 x ^{4} + e ^{x} )}{x ln ^{2} ( x ^{4} )} : \frac{( 12 x ^{4} + e ^{x} ) ( 48 x ^{4} ln ( x ) - 12 x ^{4} + e ^{x} x ln ( x ) - e ^{x} )}{8 x ln ^{3} ( x )}

= \frac{( 12 x ^{4} + e ^{x} ) ( 48 x ^{4} ln ( x ) - 12 x ^{4} + e ^{x} x ln ( x ) - e ^{x} )}{8 x ln ^{3} ( x )}

\int_{- 2}^{3} \frac{29}{x ^{4}} d x

n = 1 \sum \infty \frac{n !}{4 ^{n}}

\int (x + 1) x d x

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

\frac{\partial}{\partial x} (35 e^{5 x} y)