A person x inches tall has a pulse rate approximately given by the function. y=610x^-1/2 The instantaneous rate of change of the pulse rate for a person that is 34 inches tall is?
I know that to find this you will need to find the derivative of the original equation which I thought you could solve with the power rule to get (-1/2)(610x^-1.5) but when I tried to submit this on my homework it said that I can't raise a negative number to a negative power. I am not what to do on this,please help

Question

A person x inches tall has a pulse rate approximately given by the function. y=610x^-1/2 The instantaneous rate of change of the pulse rate for a person that is 34 inches tall is?
I know that to find this you will need to find the derivative of the original equation which I thought you could solve with the power rule to get (-1/2)(610x^-1.5) but when I tried to submit this on my homework it said that I can't raise a negative number to a negative power. I am not what to do on this,please help

anonymous · Answer

$$\frac{ dy }{ dx }=(-1/2)610 x^ {-3/2}$$
x=32

anonymous · Answer

This puts it into a non real number though. How do I solve this with a real number?

anonymous · Answer

$$(-1/2)(610)\frac{ 1 }{\sqrt[2]{32^3} }$$