derivative of (3x^2-yx+5^4)

解

\frac{d}{d x} ((3 x^{2} - y x + 5)^{4})

4 (3 x^{2} - y x + 5)^{3} (6 x - x \frac{d y}{d x} - y)

解答ステップ

\frac{d}{d x} ((3 x^{2} - y x + 5)^{4})

連鎖法則を適用:

4 (3 x^{2} - y x + 5)^{3} \frac{d}{d x} (3 x^{2} - y x + 5)

= 4 (3 x^{2} - y x + 5)^{3} \frac{d}{d x} (3 x^{2} - y x + 5)

\frac{d}{d x} (3 x^{2} - y x + 5) = 6 x - x \frac{d y}{d x} - y

= 4 (3 x^{2} - y x + 5)^{3} (6 x - x \frac{d y}{d x} - y)