Find the derivatives of the functions. s(x)=ln(x−8)−2)

djeljenike

Answered question

2021-05-18

Find the derivatives of the functions.
$s\left(x\right)={\mathrm{ln}(x-8)}^{-2})$

Answer & Explanation

Yusuf Keller

Skilled2021-05-19Added 90 answers

$s\left(x\right)={\mathrm{ln}(x-8)}^{-2})$ Simpify the logarithm first, apply ${\mathrm{ln}a}^{n}=n\mathrm{ln}a$, so $s\left(x\right)=-2\mathrm{ln}(x-8\}$ Diffetrentiate both sides with respect to x ${s}^{\prime}\left(x\right)=\frac{d}{dx}[-2\mathrm{ln}(x-8)]$ Pull out the constant ${s}^{\prime}\left(x\right)=-2\frac{d}{dx}\left[\mathrm{ln}(x-8)\right]$Apply $\frac{d}{dx}\left[\mathrm{ln}\left|u\right|\right]=\frac{1}{u}\{\frac{du}{dx}$ ${s}^{\prime}\left(x\right)=-2\left(\frac{1}{x-8}\right)\frac{d}{dx}[x-8]$ Therefore, ${s}^{\prime}\left(t\right)=-2\left(\frac{1}{x-8}\right)\left(1\right)$ $s}^{\prime}\left(x\right)=-\frac{2}{x-8$