(\partial)/(\partial x)(Q(x)0.5^{x/(35)})

解

\frac{\partial}{\partial x} (Q (x) 0. 5^{\frac{x}{35}})

0. 5^{\frac{x}{35}} \frac{\partial}{\partial x} (Q (x)) - 0.01980 \dots e^{- 0.01980 \dots x} Q (x)

解答ステップ

\frac{\partial}{\partial x} (Q (x) \cdot 0. 5^{\frac{x}{35}})

積の法則を適用:

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

f = Q (x), g = 0. 5^{\frac{x}{35}}

= \frac{\partial}{\partial x} (Q (x)) 0. 5^{\frac{x}{35}} + \frac{\partial}{\partial x} (0. 5^{\frac{x}{35}}) Q (x)

\frac{\partial}{\partial x} (0. 5^{\frac{x}{35}}) = - 0.01980 \dots e^{- 0.01980 \dots x}

= \frac{\partial}{\partial x} (Q (x)) 0. 5^{\frac{x}{35}} + (- 0.01980 \dots e^{- 0.01980 \dots x}) Q (x)

簡素化

= 0. 5^{\frac{x}{35}} \frac{\partial}{\partial x} (Q (x)) - 0.01980 \dots e^{- 0.01980 \dots x} Q (x)