derivative of ((x^2+3/(x^2-3))^3)

解答

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

- \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 3 (\frac{x ^{2} + 3}{x ^{2} - 3})^{2} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

化简

3 (\frac{x ^{2} + 3}{x ^{2} - 3})^{2} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

= - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

\int (2 x^{3} + x) (x^{4} + x^{2})^{108} d x

f (x) = sin (9 x)

\frac{d}{d x} (500 x - 2 x^{2})

x \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})