(\partial)/(\partial x)(ln(cos(x^2y^2+z)))

解

\frac{\partial}{\partial x} (ln (cos (x^{2} y^{2} + z)))

- 2 x y^{2} tan (x^{2} y^{2} + z)

解答ステップ

\frac{\partial}{\partial x} (ln (cos (x^{2} y^{2} + z)))

y, z

を定数として扱う

連鎖法則を適用:

\frac{1}{cos ( x ^{2} y ^{2} + z )} \frac{\partial}{\partial x} (cos (x^{2} y^{2} + z))

= \frac{1}{cos ( x ^{2} y ^{2} + z )} \frac{\partial}{\partial x} (cos (x^{2} y^{2} + z))

\frac{\partial}{\partial x} (cos (x^{2} y^{2} + z)) = - sin (x^{2} y^{2} + z) \cdot 2 y^{2} x

= \frac{1}{cos ( x ^{2} y ^{2} + z )} (- sin (x^{2} y^{2} + z) \cdot 2 y^{2} x)

簡素化

\frac{1}{cos ( x ^{2} y ^{2} + z )} (- sin (x^{2} y^{2} + z) \cdot 2 y^{2} x) : - 2 x y^{2} tan (x^{2} y^{2} + z)

= - 2 x y^{2} tan (x^{2} y^{2} + z)