Answer:
[tex]\frac{dy}{dt}=102[/tex]
Step-by-step explanation:
It was given that;
[tex]y=3x^3-2x[/tex]
When we differentiate this function with respect to x, we get;
[tex]\frac{dy}{dx}=9x^2-2[/tex]
When [tex]x=-2[/tex], we get;
[tex]\frac{dy}{dx}=9(-2)^2-2[/tex]
[tex]\frac{dy}{dx}=34[/tex]
Also we were given that;
[tex]\frac{dx}{dt} =3[/tex].
Recall the chain rule;
[tex]\frac{dy}{dx}=\frac{dy}{dt} \times \frac{dt}{dx}[/tex]
[tex]\Rightarrow \frac{dy}{dt}=\frac{dy}{dx} \times \frac{dx}{dt}[/tex]
We substitute these values into the formula to get;
[tex]\Rightarrow \frac{dy}{dt}=34\times 3[/tex]
[tex]\frac{dy}{dt}=102[/tex]
