(\partial)/(\partial x)(e^{-sin^2(x)}(x+c))

解

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

- e^{- s i n^{2} (x)} sin (2 x) (x + c) + e^{- s i n^{2} (x)}

解答ステップ

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

積の法則を適用:

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

f = e^{- s i n^{2} (x)}, g = x + c

= \frac{\partial}{\partial x} (e^{- s i n^{2} (x)}) (x + c) + \frac{\partial}{\partial x} (x + c) e^{- s i n^{2} (x)}

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)}) = - e^{- s i n^{2} (x)} sin (2 x)

\frac{\partial}{\partial x} (x + c) = 1

= (- e^{- s i n^{2} (x)} sin (2 x)) (x + c) + 1 \cdot e^{- s i n^{2} (x)}

簡素化

= - e^{- s i n^{2} (x)} sin (2 x) (x + c) + e^{- s i n^{2} (x)}