question suppose that the length l, width w, and area a = lw of a rectangle are differentiable functions of…

question suppose that the length l, width w, and area a = lw of a rectangle are differentiable functions of t. write an equation that relates da/dt to dl/dt and dw/dt when l = 18 and w = 13. enter your answers using exact values. provide your answer below: da/dt = □ dl/dt + □ dw/dt

question suppose that the length l, width w, and area a = lw of a rectangle are differentiable functions of t. write an equation that relates da/dt to dl/dt and dw/dt when l = 18 and w = 13. enter your answers using exact values. provide your answer below: da/dt = □ dl/dt + □ dw/dt

Answer

Explanation:

Step1: Differentiate area formula

Given $A = lw$, use the product - rule for differentiation. The product - rule states that if $y = uv$ where $u$ and $v$ are functions of $t$, then $\frac{dy}{dt}=u\frac{dv}{dt}+v\frac{du}{dt}$. Here, $u = l$ and $v = w$, so $\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}$.

Step2: Substitute given values

We are given $l = 18$ and $w = 13$. Substituting these values into the equation $\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}$, we get $\frac{dA}{dt}=18\frac{dw}{dt}+13\frac{dl}{dt}$.

Answer:

$\frac{dA}{dt}=13\frac{dl}{dt}+18\frac{dw}{dt}$