text: 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
  
  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 | 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)`
  
  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