Answer:
Therefore the rate of change of area
square inches/ s
Step-by-step explanation:
Given that,
A rectangle is growing such that the length of rectangle is(5t+4) and its height is t⁴.
Where t is in second and dimensions are in inches.
The area of a rectangle is = length× height
Therefore the area of the rectangle is
A(t) = (5t+4) t⁴
⇒A(t) = t⁴(5t+4)
To find the rate change of area we need to find out the first order derivative of the area.
Rules:


A(t) = t⁴(5t+4)
Differentiate with respect to t
![\frac{d}{dt} A(t)=\frac{d}{dt} [t^4(5t+4]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20A%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%20%5Bt%5E4%285t%2B4%5D)





Therefore the rate of change of area
square inches/ s