DOIAbstract
AbstractIt is well known that the chain-rule equation (d/dt)f(A(t))=A′(t)f′(A(t)) is valid if A(t)A′(t) =A′(t)A(t). We investigate the extent to which the converse holds
AbstractIt is well known that the chain-rule equation (d/dt)f(A(t))=A′(t)f′(A(t)) is valid if A(t)A′(t) =A′(t)A(t). We investigate the extent to which the converse holds
Calculus, derivares and Analytic GeometryThe derivative of the composition of two functions is given...
Chain rule and invariance principle on measure chains. – In: Journal of computational and applied ma...
The proof of the chain rule from calculus is usually omitted from a beginning calculus course. Six d...
AbstractIt is well known that the chain-rule equation (d/dt)f(A(t))=A′(t)f′(A(t)) is valid if A(t)A′...
This paper shows that the commutativity condition [A(t), A′(t)] = 0 is often not necessary to guara...
AbstractThe Chain Rule that expresses the derivative of exp (A(t)) as an infinite series involving i...
• We will give a definition • Prove the chain rule • Learn how to use it • Do example problems Defin...
AbstractWe consider operators T from C1(R) to C(R) satisfying the “chain rule”T(f∘g)=(Tf)∘g⋅Tg,f,g∈C...
Applies the multivariate chain rule to an example where z(x,y), x(t), y(t), to find dz/dt
AbstractWe study operators T from C1(Rn,Rn) to C(Rn,L(Rn,Rn)) satisfying the “chain rule”T(f∘g)(x)=(...
Example of using the multivariate chain rule where z=f(x,y) and x and y are both functions of t
Six short examples useful as preparation for implicit differentiation. Some require the chain rule, ...
In this perspective paper, I tried to explain that what will be the possible prospect of multiple fu...
It is demonstrated how to perform differentiation using the chain rule, side-stepping the use of new...
The chain rule for differentiation is proved from first principles. Use is made of the small differe...
Calculus, derivares and Analytic GeometryThe derivative of the composition of two functions is given...
Chain rule and invariance principle on measure chains. – In: Journal of computational and applied ma...
The proof of the chain rule from calculus is usually omitted from a beginning calculus course. Six d...
AbstractIt is well known that the chain-rule equation (d/dt)f(A(t))=A′(t)f′(A(t)) is valid if A(t)A′...
This paper shows that the commutativity condition [A(t), A′(t)] = 0 is often not necessary to guara...
AbstractThe Chain Rule that expresses the derivative of exp (A(t)) as an infinite series involving i...
• We will give a definition • Prove the chain rule • Learn how to use it • Do example problems Defin...
AbstractWe consider operators T from C1(R) to C(R) satisfying the “chain rule”T(f∘g)=(Tf)∘g⋅Tg,f,g∈C...
Applies the multivariate chain rule to an example where z(x,y), x(t), y(t), to find dz/dt
AbstractWe study operators T from C1(Rn,Rn) to C(Rn,L(Rn,Rn)) satisfying the “chain rule”T(f∘g)(x)=(...
Example of using the multivariate chain rule where z=f(x,y) and x and y are both functions of t
Six short examples useful as preparation for implicit differentiation. Some require the chain rule, ...
In this perspective paper, I tried to explain that what will be the possible prospect of multiple fu...
It is demonstrated how to perform differentiation using the chain rule, side-stepping the use of new...
The chain rule for differentiation is proved from first principles. Use is made of the small differe...
Calculus, derivares and Analytic GeometryThe derivative of the composition of two functions is given...
Chain rule and invariance principle on measure chains. – In: Journal of computational and applied ma...
The proof of the chain rule from calculus is usually omitted from a beginning calculus course. Six d...
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