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How do you find the derivative of G(x)=int (e^(t^2))dt from [1,x]?

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How do you find the derivative of G(x)=int (e^(t^2))dt from [1,x]?

You should get #e^(x^2)#.

You can use Leibniz’s integral rule.

#(dG(x))/(dx) -= d/(dx) [int_(g(x))^(h(x)) f(x,t)dt]#

#= int_(g(x))^(h(x)) (delf)/(delx)dt + f(x,h(x))(dh)/(dx) – f(x,g(x))(dg)/(dx)#

In this case, #g(x) = 1# and #h(x) = x#, so:

#(dg)/(dx) = 0#
#(dh)/(dx) = 1#
#f(x,h(x)) = f(x,t = x) = e^(x^2)#
#f(x,g(x)) = f(x,t = 1) = e^(1^2) = e#
#(delf)/(delx) = (del)/(delx)[e^(t^2)]_x = 0#


#color(blue)((dG)/(dx)) = cancel(int_(1)^(x) 0dt)^(0) + e^(x^2)cdot1 – cancel(ecdot0)#

#= color(blue)(e^(x^2))#

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Find dy/dx (dy)/(dt)=d/(dt)*(x^5+8) | Mathway – bool : Represents if element is present in vector or not. int : Represents the index of element in vector if its found else -1 */.We learn how to find the derivative of sin, cos and tan functions, and see some examples. The second one, y = cos(x2 + 3), means find the value (x2 + 3) first, then find the cosine of the result. They are quite different! Example 2.I understand that odeint gets the solution of dy/dt=func(y0,t). However, I also need to get dy/dt too. I am dealing with a structural dynamic system in which: y : displacement dy/dt : velocity d(dy/dt)/dt : acceleration (force). And I put the system into two systems

Find dy/dx (dy)/(dt)=d/(dt)*(x^5+8) | Mathway

Consider the reaction… | Yahoo Answers – If asked to find the derivative of an integral then you should not evaluate the integral but instead use the fundamental theorem of Calculus. (ie the derivative of an integral gives us the original function back). We are asked to finddir C:\ /A:DS | find "free". PS> Get-CimInstance -ComputerName bobPC win32_logicaldisk | where caption -eq "C:" | foreach-object {write " $($_.caption) $('{0:N2}' -f ($_.Size/1gb)) GB total, $('{0:N2}' -f ($_.FreeSpace/1gb)) GB free "} C: 117.99 GB total, 16.72 GB free.The meaning of d(dx/dt)/dt is well known and let us not discuss it. Your question is – how we write it for the purpose of communication. The form d2x/dt2 has been introduced by some legendary mathematician (May be Leibnitz or Newton or some one else) centuries ago, and it has stayed…

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