Question

find slope of the tangent and the normal to the curve xy=6 at (1,6)​

Answer 1

Answer:

I hope so I can do help you

Answer 2

Answer: slope=(-6)

Step-by-step explanation:

• The equation of the curve is xy=6.
• Applying log on both sides,

        log(xy)=log(6)

    ⇒ log x + log y = log 6

   differentiting both sides with respect to x

   ⇒ $\frac{1}{x} +\frac{1}{y} \frac{dy}{dx} = 0$

  ⇒ $\frac{dy}{dx}=\frac{-y}{x}$

  ⇒$\frac{dy}{dx} _{1,6} =\frac{-6}{1}$

   ∴  $\frac{dy}{dx} _{1,6} ={-6}$.

• Hence, the slope of given curve is (-6).

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