Find the second derivative of  z = 4e^5t with respect to t.  Which is the correct option from the following?Find the second derivative of  z = 4e^5t with respect to t.  Which is the correct...

Find the second derivative of  z = 4e^5t with respect to t.  Which is the correct option from the following?

Find the second derivative of  z = 4e^5t with respect to t.  Which is the correct option from the following?

d^2z/dt^2  = 100e^5t

d^2z/dt^2 = 4e^5t

d^2z/dt^2 = 20e^4t

d^2z/dt^2 = 25e^5t

d^2z/dt^2 = 20e^5t

d^2z/dt^2 = 80e^3t

Asked on by minnsy229

3 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to differentiate the given function `z(t) = 4e^(5t)`  with respect to t, using the chain rule,  such that:

`z'(t) = 4*e^(5t)*(5t)'`

`z'(t) =4*5*e^(5t)`

`z'(t) =20*e^(5t)`

You need to differentiate again the result of the first differentiation such that:

`z''(t) = (20*e^(5t))' =gt z''(t) = 20*e^(5t)*(5t)'`

`z''(t) = 20*5*e^(5t)`

`z''(t) = 100e^(5t)`

Hence, evaluating the second derivative of the function yields `z''(t) = 100e^(5t),`  hence, you need to select the first option from the given list.

Sources:
justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function `z = 4e^(5t)` . The second derivative of z with respect to t can be determined as follows:

`(dz)/(dt) = 4*5*e^(5t) = 20*e^(5t)`

`(d^2z)/(dt^2) = 20*5*e^(5t) = 100*e^(5t)`

The correct option for the second derivative of `z = 4e^(5t)` with respect to t is `(d^2z)/(dt^2) = 100*e^(5t)`

Top Answer

biditism's profile pic

biditism | Student, Undergraduate | (Level 1) Honors

Posted on

the correct answer is first one

d^2z/dt^2  = 100e^5t


Explanation:

We have a relation: d(e^at)      

                            ---------- =   a*e^at

                              dt


thus,

                             d(4e^5t)      

                            ---------- =   4*5*e^5t=20e^5t-----------A

                              dt


take the derivative of answer in A

                              d(20e^5t)      

                            ----------       =   20*5*e^5t=100e^5t

                              dt


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