I have the following problem, which requires the chain rule and can be a little tedious. I'm trying to figure out how to do this in Mathematica, but I can't get a solution. I know the answer, which is 20.085. Here's the problem:
And here's my code:
Clear[x, y, f, t] x[t_] := Sin[t]; y[t_] := Cos[t] z[t_] := 2 t^3 + 3 f[t_] := x[t] E^(y[t] z[t]) f'[t]
And Mathematica outputs the following:
E^((3 + 2 t^3) Cos[t]) Cos[t] + E^((3 + 2 t^3) Cos[t]) Sin[t] (6 t^2 Cos[t] - (3 + 2 t^3) Sin[t])
Any thought on how I can structure some code that can be used to solve other of these parameterized functions that would ordinarily require the chain rule?
Thanks so much.