What is the derivative of f(t) = (e^(t^2-1)-e^t, 2t^2-4t ) f(t)=(et21et,2t24t)?

1 Answer
Jul 8, 2016

Knowing the chain rule for derivatives, you can see that

dx/dt=2te^(t^2-1)-e^(t)dxdt=2tet21et

and

dy/dt=4t-4dydt=4t4

Thus, f'(t)=(2te^(t^2-1)-e^(t), 4t-4)

Explanation:

In this case, the "trick" is to apply the chain rule to the the first term of the expression

e^(t^2-1)-e^t

to obtain the derivative.

The chain rule formula used in this problem comes from

d/dx[e^(z)]=e^(z) dz/dx

where

z=t^2-1