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 da/dt to dl/dt and dw/dt when l = 9 and w = 10. enter your answers using exact values. da/dt = w dl/dt + l dw/dt sorry, thats incorrect. try again?

Explanation:

Step1: Recall the area formula for rectangle

$A = lw$

Step2: Differentiate both sides with respect to $t$ using the product - rule

The product - rule states that if $y = uv$, then $\frac{dy}{dt}=u\frac{dv}{dt}+v\frac{du}{dt}$. Here, $u = l$ and $v = w$. So, $\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}$

Answer:

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