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Find the derivative of y = arcsinh(1-x/1+x)derivatives

Find the derivative of y = arcsinh(1-x/1+x)derivatives

Grade:12

1 Answers

Askiitians Expert Bharath-IITD
23 Points
12 years ago

Dear Satyam,

                    we know that d/dx(arcsinh x) = 1/√(x2+1)

So here in place of x we have (1-x/1+x)

And d/dx(1-x/1+x)= [ (1+x) d/dx(1-x) - (1-x) d/dx(1+x) ] / (1+x)2

                           = [ (1+x) *(-1) - (1-x) *1 ] / (1+x)2

                           = -2/ (1+x)2

now dy/dx = 1/ √((1-x/1+x)2+1) *  d/dx(1-x/1+x)

                =[ (1+x)/√2(x2+1) ] *  -2/ (1+x)2

                      = -√2/ √(x2+1)*(1+x)

 

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Adapa Bharath
 

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