CALCULUS HELP! Relative rate of change! HELP!?

Question

Find the relative rate of change and evaluate the rate of change at the given values of t.

f(t)= e^t^3 t=5

or

f(t)= e to the power of t to the power of 3. t=5

THANK YOU! Look at all my questions... I give out BEST ANSWERS every time!!!

Answer 1

d/dx e^(f(x)) = (f '(x))e^x
therefore, the derivative (rate of change) of this problem would be (3(t^2))*(e^t^3)
then, plug in 5 for t, and you come up with
3(5^2)*(e^5^3) = 75*(e^125)

I'm assuming your teacher won't ask for an exact answer, since e is an irrational number.

Answer 2

Hello

The relative rate of change is the derivative: (3t^2)e^t^3.

Thus at t = 5 ------ we get 75(e^125) = 1.45x10^56

Answer 3

(e^t)^3 =f(t) =e^3t
f´(t) = 3 e^3t and at t=5 f´(5) = 3 e^15=9807052.117
If you meant
f(t) = e^(t^3) f´(t) = e^(t^3)*3t^2 = e^125*3*25=1.451682*10^56