derivative f(x)=4x^3sqrt(x^4)

解

導関数

f (x) = 4 x^{3} x^{4}

4 (3 x^{2} x^{4} + 2 x^{4})

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = x^{3}, g = x^{4}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 4 (3 x^{2} x^{4} + 2 x x^{3})

2 x x^{3} = 2 x^{4}

= 4 (3 x^{2} x^{4} + 2 x^{4})