(\partial)/(\partial x)(k(1+ae^{-b(x,w,t)x})(1+cos(wt)))

解

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

k (1 + cos (wt)) (0 + a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t))))

解答ステップ

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

a, k, w, t

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= k (1 + cos (wt)) \frac{\partial}{\partial x} (1 + a e^{- b (x, w, t) x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= k (1 + cos (wt)) (\frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (a e^{- b (x, w, t) x}))

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (a e^{- b (x, w, t) x}) = a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t)))

= k (1 + cos (wt)) (0 + a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t))))