Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div(F + G) = div F + div G
Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div(F + G) = div F + div G
Let k be a constant,
F
=
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y
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z
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,
G
=
G(
x
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,
and
ϕ
=
ϕ
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x
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y
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.
Prove the following identities, assuming that all derivatives involved exist and are continuous.
Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x.
A not uncommon calculus mistake is to believe that the product rule for derivatives says that (fg)′ = f′g′.
If f(x) = ex2
determine, with proof, whether there exists an open interval (a, b) and a nonzero function g defined on (a, b) such that this wrong product rule is true for x in (a, b).
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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