(\partial)/(\partial x)((14+17x)y^{tan(x)})

解

\frac{\partial}{\partial x} ((14 + 17 x) y^{t a n (x)})

17 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (14 + 17 x)

解答ステップ

\frac{\partial}{\partial x} ((14 + 17 x) y^{t a n (x)})

y

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 14 + 17 x, g = y^{t a n (x)}

= \frac{\partial}{\partial x} (14 + 17 x) y^{t a n (x)} + \frac{\partial}{\partial x} (y^{t a n (x)}) (14 + 17 x)

\frac{\partial}{\partial x} (14 + 17 x) = 17

\frac{\partial}{\partial x} (y^{t a n (x)}) = y^{t a n (x)} ln (y) sec^{2} (x)

= 17 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (14 + 17 x)