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Computing Derivative of Summation

Posted 10 years ago
 I'm trying to get used to computing derivatives within Mathematica but am unsure as to how to compute a derivative with a summation within the expression. Is there anyway someone can show me how to compute the derivative of the following function using commands in Mathematica? f (x) = Summation [ ke^-(ax^3)] with k min = 1, k max = 7] with a being a constant Do I need to define a as a constant prior? Any ideas? The answer should come out to -3akx^2
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Posted 10 years ago
 Will the following be sufficient? It has the derivative term, multiplied by the result of the summation where the limits have been parametrized.In Clear["Global"]; ( Clear. *)s[x_] := Sum[ k Exp[-a x^3], {k, m, n}]; (* Define the expression. *)D[ s[x], x] (* Find Derivative. *)Out[140]= 3/2 a E^(-a x^3) (-1 + m - n) (m + n) x^2When m and n are assigned values, we will get back a single expression.In[141]:= % /. {m -> 1, n -> 7}Out[141]= -84 a E^(-a x^3) x^2
Posted 10 years ago
 Wait you're right about the exponential! However, the answer should come off as -summation (k = 1 to k = 7) 3kax^2e^-(a^3)but what you gave isn't correct - do I need to state that a is a constant prior?
Posted 10 years ago
 The answer should come out to -3akx^2 What happend to exp() function in the answer? This is what Mathematica gives  Clear[x, a, k] f = Sum[ k Exp[-a x^3], {k, 1, 7} ]; D[f, x] (* (-84*a*x^2)/E^(a*x^3) *) There is no need to define a function f[x] in here. it is just an expression. But this also works  Clear[x, a, k] f[x_] := Sum[ k Exp[-a x^3], {k, 1, 7} ]; D[f[x], x] `