Find all the antiderivatives of the following function. Check your work by taking derivatives. f(x)=ex

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Find all the antiderivatives of the following function. Check your work by taking derivatives.  f(x)=ex

FieniChoonin · Accepted Answer

Step 1Given.f(x)=exThe objective is to find all the antiderivatives of the given function Step 2On considering the function f(x) in an interval l then the differentiation of function f(x) is called derivative off&#039;(x)A function F(x) is said to be anti derivative of the function f(x) on considering F&#039;(x)=f(x) for all here x tends to IOn considering F(x) be any anti derivative of f(x) on an interval l. Then all the anti derivative of f(x) on the interval I have the form F(x)+c where, c is an arbitrary constantStep 3Here on considering the function ex the differentiation is defined as follows,ddxex=ex  for all n tends to RTherefore,ddxex=exHere the derivative of the function f(x)=ex is exAccording to the theorem mentioned above the complete family of anti derivative will be as follows,F(x)=ex+CWhere.C is the arbitrary constant

Find all the antiderivatives of the following function. Check your work by taking derivatives. f(x)=e^{x}

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