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Find the function from its given derivative

f(x)=2x14x2

Short Answer

Expert verified

The function from its given derivative is

f(x)=1214x2

Step by step solution

01

Step 1.Given information

WE have been given the derivative of function

f(x)=2x14x2

02

Step 2.We have been finding the function whose derivative is given 

One can suspect thesin1xfrom the denominator of function

f(x)=sin1(2x)f(x)=sin1(2x)f(x)=11(2x)2ddx(2x)=214x2
03

Step 3.Finding the more appropriate function from previous one 

Now , letting the functionf(x)=1214x2

f(x)=1214x2f(x)=12ddx14x212=121214x212ddx14x2ddxxn=nxn1=1414x2ddx1ddx4x2=1A14x2(A(2x))=2x14x2=2x14x2

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