(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

It is given that, [tex]\left(e^{-t^2}y\right)'=e^{-t^2}\left(y'-2ty\right)[/tex], which I am trying to work out.

2. Relevant equations

[tex]f'(t)=h'(g(t))g'(t)[/tex]

[tex](u\cdot v)'=u'v+uv'[/tex]

3. The attempt at a solution

[tex]f(t)=e^{-t^2}y=h(g(t))[/tex]

[tex]\text{let}\;g(t)=u=t^2\;\text{and}\;h(u)=e^{-u}y[/tex]

[tex]\text{thus}\;g'(t)=2t[/tex]

[tex]h'(u)=\left(e^{-u}y\right)'=e^{-u}\dfrac{dy}{du}-e^{-u}y[/tex]

Hence,

[tex]f'(t)=\left[e^{-t^2}y'-e^{-t^2}y\right]\cdot 2t[/tex]

This does not match the expected solution; your help would be much appreciated!

Cheers

Mike

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# Homework Help: Chain rule annoyance

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