Question

Let $u = x^2y^3$, $v = \sin(\pi x)$ and $z = f(u, v)$ where $f$ is a function with continuous first order partial derivatives such that $f_u(1, 0) = \frac{1}{3}$, $f_v(1, 0) = \frac{1}{\pi}$. Then what is $\frac{\partial z}{\partial x}|_{(x, y) = (2, \frac{1}{2})} + \frac{\partial z}{\partial y}|_{(x, y) = (2, \frac{1}{2})}$?

Name: Let u = x^2y^3, v = sin(π x) and z = f(u, v) where f is a function with continuous first order partial derivatives such that fu(1, 0) = (1)/(3), fv(1, 0) = (1)/(π). Then what is (∂ z)/(∂ x)|(x, y) = (2, (1)/(2)) + (∂ z)/(∂ y)|(x, y) = (2, (1)/(2))?
Uploaded: 2023-07-19T03:59:11-08:00
Duration: 5 min 8 s
Channel: Madhur L
Description: Let u = x^2y^3, v = sin(π x) and z = f(u, v) where f is a function with continuous first order partial derivatives such that fu(1, 0) = (1)/(3), fv(1, 0) = (1)/(π). Then what is (∂ z)/(∂ x)|(x, y) = (2, (1)/(2)) + (∂ z)/(∂ y)|(x, y) = (2, (1)/(2))?

          Let $u = x^2y^3$, $v = \sin(\pi x)$ and $z = f(u, v)$ where $f$ is a function with continuous first order partial derivatives such that $f_u(1, 0) = \frac{1}{3}$, $f_v(1, 0) = \frac{1}{\pi}$. Then what is $\frac{\partial z}{\partial x}|_{(x, y) = (2, \frac{1}{2})} + \frac{\partial z}{\partial y}|_{(x, y) = (2, \frac{1}{2})}$?