Originally Posted by

**starswept** Hello, back again with another derivatives question:

A grocery store determines that after t hours on the job, a new cashier can ring up N(t) = 20 - (30

÷

√(9 + t^2)

items per minute. Find N' (t), the rate at which the cashier's productivity is changing.

I've solved the derivative to

(9 + t^2)^(1/2) - 30 t

÷

(9+t^2)^(3/2)

But the correct answer should be simply

30 t

÷

(9 + t^2)^(3/2)

I have no idea how the (9 + t^2)^(1/2) in the numerator vanishes, though I've tried re-doing it several times. I'd greatly appreciate it if anyone could show me the steps to simplifying this derivative. Thank you in advance!