Another differentiation problem

[b521]

Homework Statement

If z² = x² + y²
and
dx/dt = 2
and
dy/dt = 3

Find dz/dt when x=5 and y=12

Homework Equations

I used

The Attempt at a Solution

But I resulted in:

2z dz/dt = 2x(dx/dt) + 2y(dy/dt)

Plugged in x,y,dx/dt, and dy/dt to get:

2z (dz/dt) = 2(5)(2) + 2(12)(3)

dz/dt = 80/2z
= 40/z
But the answer is +/- 46/13

Anyone know where I went wrong?

 

[Mark44]

Homework Statement

If z² = x² + y²
and
dx/dt = 2
and
dy/dt = 3

Find dz/dt when x=5 and y=12

Homework Equations

I used

The Attempt at a Solution

But I resulted in:

2z dz/dt = 2x(dx/dt) + 2y(dy/dt)

Plugged in x,y,dx/dt, and dy/dt to get:

2z (dz/dt) = 2(5)(2) + 2(12)(3)

dz/dt = 80/2z
= 40/z



But the answer is +/- 46/13

5*2 + 12*3 = 46, not 40. Also, when x = 5 and y = 12, z = +/- 13.

Anyone know where I went wrong?

 

[b521]

Ahhh thank you very much!