Increasing Function: Finding k When x=pi/4

[coookiemonste]

Homework Statement

When x=pi/4, the rate at which sinx^2 is increasing is k times the rate at which x is increasing. What is the value of k?
(answer is 1)

Homework Equations

The Attempt at a Solution

I plugged in pi/4 into sinx^2 and i got .5.
i also took the derivative of sinx^2 and plugged in pi/4 to get the slope, which is 1.
So it seems to me that I found the rate at which sinx^2 is increasing (1), but i don't know how to find the rate at which x is increasing.
do i just take an average slope?

 

[dx]

Hint: (dy/dt) / (dx/dt) = dy/dx.

 

[coookiemonste]

i think dy/dt would be 1.
how do i find dx/dt?

 

[dx]

dx/dt is not given and is not needed. You only know that the ratio dy/dt and dx/dt is k. But the ratio of dy/dt and dx/dt is dy/dx, so what does that tell you?

 

[coookiemonste]

that it is just simply the slope of sinx^2 when x=pi/4
which is 1
?

 

[dx]

Yes, that's right.