If x2 + y2 + z2 = 9, dxdt = 4, and dydt = 8, find dzdt when (x, y, z) = (2, 2, 1).
Question
Solution 1
To solve this problem, we need to use the chain rule of differentiation.
Given the equation x² + y² + z² = 9, we can differentiate both sides with respect to t to get:
2x(dx/dt) + 2y(dy/dt) + 2z(dz/dt) = 0.
We know that dx/dt = 4, dy/dt = 8, and we are trying to find dz/dt. We also know that at Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI
Similar Questions
If x2 + y2 + z2 = 9, dxdt = 4, and dydt = 8, find dzdt when (x, y, z) = (2, 2, 1).
If x,y,z∈R, x+y+z=5, x2+y2+z2=9𝑥,𝑦,𝑧∈𝑅, 𝑥+𝑦+𝑧=5, 𝑥2+𝑦2+𝑧2=9, then length of interval in which x𝑥 lies is
Simplify the following expression: (x + y + z)2 + (x + y2 + z3 )2 - ( x2 + y3 + z4 )
Suppose 4x2 + 16y2 = 100, where x and y are functions of t.(a)If dydt = 14, find dxdt when x = 3 and y = 2.
Find the volume of the given solid.Bounded by the cylinders x2 + y2 = 16r2, y2 + z2 = 16r2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.