derivative of ((x^2-9/(4x+5))^4)

解答

\frac{d}{d x} ((\frac{x ^{2} - 9}{4 x + 5})^{4})

\frac{4 ( x ^{2} - 9 ) ^{3} ( 4 x ^{2} + 10 x + 36 )}{( 4 x + 5 ) ^{5}}

求解步骤

\frac{d}{d x} ((\frac{x ^{2} - 9}{4 x + 5})^{4})

使用连锁律:

4 (\frac{x ^{2} - 9}{4 x + 5})^{3} \frac{d}{d x} (\frac{x ^{2} - 9}{4 x + 5})

= 4 (\frac{x ^{2} - 9}{4 x + 5})^{3} \frac{d}{d x} (\frac{x ^{2} - 9}{4 x + 5})

\frac{d}{d x} (\frac{x ^{2} - 9}{4 x + 5}) = \frac{4 x ^{2} + 10 x + 36}{( 4 x + 5 ) ^{2}}

= 4 (\frac{x ^{2} - 9}{4 x + 5})^{3} \frac{4 x ^{2} + 10 x + 36}{( 4 x + 5 ) ^{2}}

化简

4 (\frac{x ^{2} - 9}{4 x + 5})^{3} \frac{4 x ^{2} + 10 x + 36}{( 4 x + 5 ) ^{2}} : \frac{4 ( x ^{2} - 9 ) ^{3} ( 4 x ^{2} + 10 x + 36 )}{( 4 x + 5 ) ^{5}}

= \frac{4 ( x ^{2} - 9 ) ^{3} ( 4 x ^{2} + 10 x + 36 )}{( 4 x + 5 ) ^{5}}

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