Question

answer the question I will mark u as brain list​

Answer 1

Hi there!
Here's the answer:

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¶¶¶ POINTS TO REMBER:

• $\dfrac{d}{dx}\, x^{n}=nx^{n-1}$

• $\dfrac{a^{m}}{a^{n}}= a^{m-n}$

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¶¶¶ SOLUTION:

Given,
$\left(\dfrac{x}{a}\right)^n+\left(\dfrac{y}{b}\right)^n = 2$

$\left(\dfrac{1}{a^n}\right)x^n+\left(\dfrac{y}{b^n}\right)y^n= 2$

Differentiate w.r.t x on both sides

$\left(\dfrac{1}{a^n}\right)n \cdot x^{n-1}+\left(\dfrac{y}{b^n}\right)n \cdot y^{n-1}\cdot \dfrac{dy}{dx}= 0$

Substitute x = a and y = b to find Derivative at (a,b)

$\implies \dfrac{na^{n-1}}{a^{n}}+\dfrac{nb^{n-1}}{b^{n}}\cdot\dfrac{dy}{dx}$

$\implies na^{n-1-n}+nb^{n-1-n}\cdot\dfrac{dy}{dx}$

$\implies na+nb\cdot\dfrac{dy}{dx}=0$

$\implies nb\cdot\dfrac{dy}{dx} = -na$

$\implies \dfrac{dy}{dx}_{(a,b)}=\dfrac{-a}{b}$

This answer is in option -2

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Answer 2

¶¶¶ POINTS TO REMBER:

•

•

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¶¶¶ SOLUTION:

Given,

Differentiate w.r.t x on both sides

Substitute x = a and y = b to find Derivative at (a,b)

This answer is in option -2