d/(dθ)(ln({x}(θ))(-θ-2))

解

\frac{d}{d θ} (ln (x (θ)) (- θ - 2))

\frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))

解答ステップ

\frac{d}{d θ} (ln (x (θ)) (- θ - 2))

積の法則を適用:

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

f = ln (x (θ)), g = - θ - 2

= \frac{d}{d θ} (ln (x (θ))) (- θ - 2) + \frac{d}{d θ} (- θ - 2) ln (x (θ))

\frac{d}{d θ} (ln (x (θ))) = \frac{\frac{d}{d θ} ( x ( θ ) )}{x ( θ )}

\frac{d}{d θ} (- θ - 2) = - 1

= \frac{\frac{d}{d θ} ( x ( θ ) )}{x ( θ )} (- θ - 2) + (- 1) ln (x (θ))

簡素化

\frac{\frac{d}{d θ} ( x ( θ ) )}{x ( θ )} (- θ - 2) + (- 1) ln (x (θ)) : \frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))

= \frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))