Question

The sides of a square are increasing at a rate of 5 m/s. the area of the square is changing at a rate of (blank) m/s^2 when the sides are 30m long.

Answer 1

Okay start with: \[
A=x^2
\]

Answer 2

Can you implicitly differentiate this equation with respect to \(t\)?

Answer 3

length = 5(t) + length of original side

area = length^2

dl/dt = 5

da/dl = 2(L)

Answer 4

da/dt = 10(L)

Answer 5

Don't come up with any explicit equations of \(t\).

Answer 6

dA/dx = 2x

Answer 7

Correct.

Answer 8

I would think the sides are changing at a rate of 2(x) where x = 30 = length of side

Answer 9

= 60

Answer 10

\[
A'=2xx'=2(30)(5)
\]

Answer 11

oh because x is a function of time?

Answer 12

Yes.

Answer 13

\[
\frac{dA}{dt}=\frac{dA}{dx}\frac{dx}{dt}
\]

Answer 14

Thanks

Answer 15

oh because x is a function of time?

Answer 16

Yeah

Answer 17

Well you just have to remember that derivatives is all about which variable you differentiate.