derivative 2x^4sqrt(25-x^2)

解

導関数

2 x^{4} 25 - x^{2}

\frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

解答ステップ

\frac{d}{d x} (2 x^{4} 25 - x^{2})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{4} 25 - x^{2})

積の法則を適用:

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

f = x^{4}, g = 25 - x^{2}

= 2 (\frac{d}{d x} (x^{4}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4})

簡素化

2 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4}) : \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

= \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}