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partial derivative of te^{(w/t})

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∂ ∂ t (te^(wt ))

Solution

e^wt−e^wtwt

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Solution steps

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∂ ∂ t (te^(wt ))

Treat w as a constant

Apply the Product Rule: (f·g)′=f ′·g+f·g′

f=t, g=e^wt

=∂ ∂ t (t)e^wt+∂ ∂ t (e^wt)t

∂ ∂ t (t)=1

∂ ∂ t (e^wt)=−we^wtt²

=1· e^wt+(−we^wtt² )t

Simplify 1· e^wt+(−we^wtt² )t: e^wt−e^wtwt

=e^wt−e^wtwt

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

partial derivative of te^{(w/t})

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