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

1 Answer
Nov 9, 2016

(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)