(\partial)/(\partial x)(sec^5(x^3y^3))

解

\frac{\partial}{\partial x} (sec^{5} (x^{3} y^{3}))

15 x^{2} y^{3} sec^{5} (x^{3} y^{3}) tan (x^{3} y^{3})

解答ステップ

\frac{\partial}{\partial x} (sec^{5} (x^{3} y^{3}))

y

を定数として扱う

連鎖法則を適用:

5 (sec (x^{3} y^{3}))^{4} \frac{\partial}{\partial x} (sec (x^{3} y^{3}))

= 5 (sec (x^{3} y^{3}))^{4} \frac{\partial}{\partial x} (sec (x^{3} y^{3}))

\frac{\partial}{\partial x} (sec (x^{3} y^{3})) = sec (x^{3} y^{3}) tan (x^{3} y^{3}) \cdot 3 y^{3} x^{2}

= 5 (sec (x^{3} y^{3}))^{4} sec (x^{3} y^{3}) tan (x^{3} y^{3}) \cdot 3 y^{3} x^{2}

簡素化

5 sec^{4} (x^{3} y^{3}) sec (x^{3} y^{3}) tan (x^{3} y^{3}) \cdot 3 y^{3} x^{2} : 15 x^{2} y^{3} sec^{5} (x^{3} y^{3}) tan (x^{3} y^{3})

= 15 x^{2} y^{3} sec^{5} (x^{3} y^{3}) tan (x^{3} y^{3})