Question

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 $\frac{da}{dt}$ to $\frac{dl}{dt}$ and $\frac{dw}{dt}$ when $l = 18$ and $w = 13$. enter your answers using exact values. provide your answer below: $\frac{da}{dt}=\frac{dl}{dt}square+\frac{dw}{dt}square$

Explanation:

Step1: Recall the product - rule for differentiation

The area of a rectangle is $A = lw$. By the product - rule of differentiation, if $A(t)=l(t)w(t)$, then $\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}$.

Answer:

$w\frac{dl}{dt}+l\frac{dw}{dt}$