Question

Suppose that a dimension x and the area A of a shape are differentiable functions of t. Write an equation that relates to .

Answer 1

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)