Respuesta :
Complete question is;
Suppose that a dimension x and the area A = 2x² of a shape are differentiable functions of t. Write an equation that relates dA/dt to dx/dt.
Answer:
Step-by-step explanation:
Since A = 2x²
Let's differentiate both sides with respect to x.
dA/dx = 4x
Now, we want to find the relationship between dA/dt and dx/dt
dA/dt can be expressed as;
(dA/dt) = (dA/dx) × (dx/dt)
Thus;
dA/dt = 4x(dx/dt)
Thus, the equation that relates dA/dt to dx/dt is;
dA/dt = 4x(dx/dt)
The equation that relates dA/dt to dx/dt is dA/dt=4x(dx/dt).
The question is looks like incomplete question
Complete question is;
Suppose that a dimension x and the area A = 2x² of a shape are differentiable functions of t. Write an equation that relates dA/dt to dx/dt.
We have given that the xis dimension and A = 2x²
What is the meaning of differentiation?
Differentiation means the rate of change of area with respect to x.
differentiate both sides with respect to x so we get,
[tex]\frac{dA}{dx} = 4x[/tex]
Now, we want to find the relationship between [tex]dA/dt[/tex] and [tex]dx/dt[/tex]
[tex]dA/dt[/tex] can be expressed as;
[tex]\frac{dA}{dt} =\frac{dA}{dx} \times \frac{dx}{dt}[/tex]
[tex]dA/dt = 4x(dx/dt).....(Since, dA/dx=4x)[/tex]
Thus, the equation that relates [tex]dA/dt[/tex] to[tex]dx/dt[/tex] is;
[tex]dA/dt = 4x(dx/dt)[/tex]
Therefore from the given the equation is dA/dt=4x(dx/dt).
To learn more about the differentiation visit:
https://brainly.com/question/25081524
