derivative x^2sqrt(49-x^2)

解答

导数

x^{2} 49 - x^{2}

\frac{- 3 x ^{3} + 98 x}{49 - x ^{2}}

求解步骤

\frac{d}{d x} (x^{2} 49 - x^{2})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 49 - x^{2}

= \frac{d}{d x} (x^{2}) 49 - x^{2} + \frac{d}{d x} (49 - x^{2}) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (49 - x^{2}) = - \frac{x}{49 - x ^{2}}

= 2 x 49 - x^{2} + (- \frac{x}{49 - x ^{2}}) x^{2}

化简

2 x 49 - x^{2} + (- \frac{x}{49 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 98 x}{49 - x ^{2}}

= \frac{- 3 x ^{3} + 98 x}{49 - x ^{2}}

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