(\partial)/(\partial x)(tan(3x^2+2x))

解

\frac{\partial}{\partial x} (tan (3 x^{2} + 2 x))

sec^{2} (3 x^{2} + 2 x) (6 x + 2)

解答ステップ

\frac{\partial}{\partial x} (tan (3 x^{2} + 2 x))

連鎖法則を適用:

sec^{2} (3 x^{2} + 2 x) \frac{\partial}{\partial x} (3 x^{2} + 2 x)

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

\frac{\partial}{\partial x} (3 x^{2} + 2 x) = 6 x + 2

= sec^{2} (3 x^{2} + 2 x) (6 x + 2)