Let f be a differentiable function of one variable, and let w = f ρ , where ρ = x 2 + y 2 + z 2 1 / 2 . show that ∂ w ∂ x 2 + ∂ w ∂ y 2 + ∂ w ∂ z 2 = d w d ρ 2
Let f be a differentiable function of one variable, and let w = f ρ , where ρ = x 2 + y 2 + z 2 1 / 2 . show that ∂ w ∂ x 2 + ∂ w ∂ y 2 + ∂ w ∂ z 2 = d w d ρ 2
Let f be a differentiable function of one variable, and let
w
=
f
ρ
,
where
ρ
=
x
2
+
y
2
+
z
2
1
/
2
.
show that
∂
w
∂
x
2
+
∂
w
∂
y
2
+
∂
w
∂
z
2
=
d
w
d
ρ
2
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂ f/∂y= ∂g/∂y for every point(x, y) ∈ R2. What is the relationship between f and g?
dw
dw
and
dv
Sxpress du
as a function of u and v
w = Xy + XZz + XZ where x = u + v and y = u-v
and then evaluate at point (u.v)=(1/2, 1)
Let f(x.y.z) be a function that satisfies
fx(1,-2,3)=1, fy(1,-2.3)=-3 and f-(1,-2,3)=2.
What is the value of the directional derivative Duf(1,-2.3) where u=4i+3k ?
O a. 2
Ob. 10
O.O
O d.-5
Thomas' Calculus: Early Transcendentals (14th Edition)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY