Question about using derivatives

[Cbray]

Homework Statement

Find the approximate percentage changes in the given function y = f(x) that will result from an increase of 2%
y = x²

Homework Equations

The Attempt at a Solution

dy/dt = dx/dt * d/dx * x²
dy/dt = dx/dt * 2x
dy/dt = 2/100 * 2x
dy/dt = 4x% ? I don't know if I did this right but apparently in the back of the book I'm not suppose to have the x in there, why not?

 

[hvidales]

Would it be because your supposed to take the second derivative of it? That would make it just 2. I think as the question wants no variables in it too.

 

[Cbray]

Would it be because your supposed to take the second derivative of it? That would make it just 2. I think as the question wants no variables in it too.

I don't think that is correct...

 

[Pengwuino]

What is 't'? You have $y = x^2$ and x seems to have no dependence on a parameter 't'. You simply need to determine ${{dy}\over{dx}}$

And no, there are no second derivatives involved.

 

[Cbray]

What is 't'? You have $y = x^2$ and x seems to have no dependence on a parameter 't'. You simply need to determine ${{dy}\over{dx}}$

And no, there are no second derivatives involved.

Do you mind filling me in a bit more, i.e. is my working wrong apart from that

 

[micromass]

Do you mind filling me in a bit more, i.e. is my working wrong apart from that

There is not really a working apart from that. So no, it's not correct.

 

[Cbray]

[solved]
dy/dx=2x
dy/y=2x dx/x²
dy/y=2 * 2/100
dy/y = 4%