derivative of 5x^2(x+47)

解

\frac{d}{d x} (5 x^{2} (x + 47))

5 (3 x^{2} + 94 x)

解答ステップ

\frac{d}{d x} (5 x^{2} (x + 47))

定数を除去:

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

= 5 \frac{d}{d x} (x^{2} (x + 47))

積の法則を適用:

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

f = x^{2}, g = x + 47

= 5 (\frac{d}{d x} (x^{2}) (x + 47) + \frac{d}{d x} (x + 47) x^{2})

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

\frac{d}{d x} (x + 47) = 1

= 5 (2 x (x + 47) + 1 \cdot x^{2})

簡素化

5 (2 x (x + 47) + 1 \cdot x^{2}) : 5 (3 x^{2} + 94 x)

= 5 (3 x^{2} + 94 x)