What is the derivative of #f(t) = (t +e^t, te^t-t^2+t ) #?

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What is the derivative of #f(t) = (t +e^t, te^t-t^2+t ) #?

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Answer 1 · 2016-11-09T07:39:52

#(te^t + e^t - 2t + 1 )/ (1 + e^t) #

Explanation:

Differentiation states #dy/dx#

#x= t+ e^t#
#y= te^t-t^2+t#

Take the derivative of both functions
#x'= 1 + e^t #
#y'= d/dt (te^t) - d/dt(t^2) + d/dt (t) #
Use product rule for #te^t#, which states: f' g + f g'
#d/dt (t) * e^t + t * d/dt (e^t) - 2t + 1 #

#1 * e^t + t * e^t - 2t +1 #

#y'=te^t + e^t - 2t + 1 #

so now #dy/dx#

#(te^t + e^t - 2t + 1 )/ (1 + e^t) #

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What is the derivative of #f(t) = (t +e^t, te^t-t^2+t ) #?

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