Question

if x3+y3=10 then the value of dy/dx​

Answer 1

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Answer 2

We have:

$x^3+y^3=10$

We have to find the value of $\dfrac{dy}{dx} .$

Solution:

$x^3+y^3=10$

Differentiating both sides w.r.t. x, we get

$\dfrac{d}{dx} {(x^3+y^3)}=\dfrac{d}{dx}(10)$

⇒ $\dfrac{d}{dx} {(x^3)+\dfrac{d}{dx}(y^3)}=\dfrac{d}{dx}(10)$

⇒ $3x^2+3y^2\dfrac{dy}{dx}}=0$

⇒ $3y^2\dfrac{dy}{dx}}=-3x^2$

⇒ $\dfrac{dy}{dx}}=-\dfrac{x^2}{y^2}$

Thus, the value of $\dfrac{dy}{dx}$ is equal to $-\dfrac{x^2}{y^2}.$