Question-119565

Question Number 119565 by bemath last updated on 25/Oct/20

Commented by bemath last updated on 25/Oct/20

g a v e k u d o s

Answered by TANMAY PANACEA last updated on 25/Oct/20

y = {l o g}_{7} {(\frac{x + 6}{x + 6})}^{l n 7}

y = l n 7 \times \frac{l n (\frac{x + 6}{x - 6})}{l n 7} [{l o g}_{a} b = \frac{l o g b}{l o g a})

y = l n (x + 6) - l n (x - 6)

\frac{d y}{d x} = \frac{1}{x + 6} - \frac{1}{x - 6} = \frac{x - 6 - x - 6}{(x + 6) (x - 6)}

\frac{d y}{d x} = \frac{- 12}{(x + 6) (x - 6)}

Answered by Ar Brandon last updated on 25/Oct/20

y = \log_{7} [{(\frac{x + 6}{x - 6})}^{\ln 7}]

7^{y} = {(\frac{x + 6}{x - 6})}^{\ln 7} = {(1 + \frac{12}{x - 6})}^{\ln 7}

\Rightarrow 7^{y} \ln 7 \frac{dy}{dx} = - \ln 7 \frac{12}{{(x - 6)}^{2}} {(\frac{x + 6}{x - 6})}^{\ln 7 - 1}

\Rightarrow 7^{y} \frac{dy}{dx} = - \frac{12}{(x - 6) (x + 6)} {(\frac{x + 6}{x - 6})}^{\ln 7}

\Rightarrow \frac{dy}{dx} = \frac{- 12}{(x - 6) (x + 6)}