Respuesta :

LammettHash
[tex]x^2(y-6)=12y+3[/tex]

Differentiate:

[tex]2x\dfrac{\mathrm dx}{\mathrm dt}(y-6)+x^2\dfrac{\mathrm dy}{\mathrm dt}=12\dfrac{\mathrm dy}{\mathrm dt}[/tex]

Plug in everything you know: [tex]\dfrac{\mathrm dy}{\mathrm dt}=2[/tex], [tex]x=5[/tex], and [tex]y=12[/tex]

[tex]2(5)\dfrac{\mathrm dx}{\mathrm dt}(12-6)+5^2(2)=12(2)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{13}{30}[/tex]

The value of dx/dt at given conditions is -13/30.

How is dx/dt calculated?

Given Equation:

[tex]x^{2} (y-6)=12y+3[/tex]

With the help of chain rule, we will differentiate the above eqn.

Differentiation of eqn w.r.t to t:

[tex]2x\dfrac{dx}{dt}(y-6)+x^{2}\dfrac{dy}{dt}=12\dfrac{dy}{dt}[/tex]      {Since x and y are functions of t}

Given:

x=5, y=12, dy/dt=2  ,put values in above eqn.

[tex]2(5)\dfrac{dx}{dt}(12-6)+5^{2}(2) =12(2)\\\\ 60\dfrac{dx}{dt}=-26\\\\\dfrac{dx}{dt}=\dfrac{-13}{30}[/tex]

Therefore value of dx/dt is -13/30.

To know more about differentiation: https://brainly.in/question/1238773

#SPJ2

Otras preguntas