derivative of sqrt(3+4x^2+9x^4)

解答

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

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

求解步骤

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

使用连锁律:

\frac{1}{2 3 + 4 x ^{2} + 9 x ^{4}} \frac{d}{d x} (3 + 4 x^{2} + 9 x^{4})

= \frac{1}{2 3 + 4 x ^{2} + 9 x ^{4}} \frac{d}{d x} (3 + 4 x^{2} + 9 x^{4})

\frac{d}{d x} (3 + 4 x^{2} + 9 x^{4}) = 36 x^{3} + 8 x

= \frac{1}{2 3 + 4 x ^{2} + 9 x ^{4}} (36 x^{3} + 8 x)

化简

\frac{1}{2 3 + 4 x ^{2} + 9 x ^{4}} (36 x^{3} + 8 x) : \frac{2 x ( 9 x ^{2} + 2 )}{3 + 4 x ^{2} + 9 x ^{4}}

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

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