derivative of 5xsqrt(64-x^2)

解

\frac{d}{d x} (5 x 64 - x^{2})

\frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

解答ステップ

\frac{d}{d x} (5 x 64 - x^{2})

定数を除去:

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

= 5 \frac{d}{d x} (x 64 - x^{2})

積の法則を適用:

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

f = x, g = 64 - x^{2}

= 5 (\frac{d x}{d x} 64 - x^{2} + \frac{d}{d x} (64 - x^{2}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (64 - x^{2}) = - \frac{x}{64 - x ^{2}}

= 5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

簡素化

5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

= \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}