(\partial)/(\partial x)(2ysin(x)-x^3+ln(y))

解

\frac{\partial}{\partial x} (2 y sin (x) - x^{3} + ln (y))

- 3 x^{2} + 2 y cos (x)

解答ステップ

\frac{\partial}{\partial x} (2 y sin (x) - x^{3} + ln (y))

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (2 y sin (x)) - \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (ln (y))

\frac{\partial}{\partial x} (2 y sin (x)) = 2 y cos (x)

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

\frac{\partial}{\partial x} (ln (y)) = 0

= 2 y cos (x) - 3 x^{2} + 0

簡素化

= - 3 x^{2} + 2 y cos (x)