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#### DeusAbscondus

##### Active member

- Jun 30, 2012

- 176

I have attached a pdf setting forth my question.

This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard:

$Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now $$(fog)'(x)=f'(g(x))=f'(g(x)).g'(x)$

$f'(y)=e^{y}$

$g'(x)=2$

$(fog)'(x)=f'(2x).2=2e^{2x}$

My approach to solving problems like this has been unsystematic; he has tried to get me to think about these chain-rule problems in terms of function notation, rather than the unseemly parade of variables I trade in, as can be seen below

$\text{Now if: }y=x^2.e^{-x} \text{then let: }f(x)=x^2; g(x)=e^{-x};y'=f'(x).g'(x)=2x.-e^{-x}$

Would someone kindly comment critically and with explanations on the two formats/usages and their relative strengths/weaknesses as a modus operandi for all such problems, at the level of beginner.

Thanks,

DeusAbs

This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard:

$Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now $$(fog)'(x)=f'(g(x))=f'(g(x)).g'(x)$

$f'(y)=e^{y}$

$g'(x)=2$

$(fog)'(x)=f'(2x).2=2e^{2x}$

My approach to solving problems like this has been unsystematic; he has tried to get me to think about these chain-rule problems in terms of function notation, rather than the unseemly parade of variables I trade in, as can be seen below

$\text{Now if: }y=x^2.e^{-x} \text{then let: }f(x)=x^2; g(x)=e^{-x};y'=f'(x).g'(x)=2x.-e^{-x}$

Would someone kindly comment critically and with explanations on the two formats/usages and their relative strengths/weaknesses as a modus operandi for all such problems, at the level of beginner.

Thanks,

DeusAbs

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