The discussion centers on a differentiation problem involving the equation z² = x² + y², where dx/dt = 2 and dy/dt = 3. The user attempted to find dz/dt by applying implicit differentiation but arrived at an incorrect conclusion. The correct approach reveals that when x = 5 and y = 12, z equals +/- 13, leading to the correct result of dz/dt being +/- 46/13, not 40/z as initially calculated.
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5*2 + 12*3 = 46, not 40. Also, when x = 5 and y = 12, z = +/- 13.b521 said: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
b521 said:
