derivative of x^3+ky(x^2-5xy)

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (k y (x) x^{2}) = k (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x))

\frac{d}{d x} (5 x y (x)) = 5 (y (x) + x \frac{d}{d x} (y (x)))

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