Question

If y = 3x^3 - 2x and dx/dt equals 3, find dy/dt when x = -2. Give only the numerical answer. For example, if dy, dt = 4, type only 4.

Answer 1

Answer:

 $\frac{dy}{dt} = 102$

Step-by-step explanation:

step(i)

Given function y = 3 x³ - 2 x  ... (i)

Differentiating equation (i) with respective to 'x'

    $\frac{dy}{dx} = 3 (3 x^{2} ) - 2(1)$

Given x = -2

$(\frac{dy}{dx} ) x_{=-2} = 3 (3 (-2)^{2} ) - 2(1)$

$(\frac{dy}{dx} ) x_{=-2} = 36 -2 =34$

Step(ii):-

we know that

                     $\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

Given    $\frac{dx}{dt} = 3 and \frac{dy}{dx} = 34$

                  $\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

substitute values    $\frac{dx}{dt} = 3 and \frac{dy}{dx} = 34$  

           ⇒        $34 = \frac{\frac{dy}{dt} }{3 }$

cross multiplication , we get

                      $\frac{dy}{dt} = 34( 3 ) = 102$

Final answer:-

 $\frac{dy}{dt} = 34( 3 ) = 102$