Please Solve this!!

Question

Find the derivative of f(x)= x + 1/x by first principle!

Answer 1

Only the numerator:

x + h + 1/(x+h) - (x + 1/x)

x + h + 1/(x+h) - x - 1/x

h + 1/(x+h) - 1/x

h + x/x(x+h) - (x+h)/x(x+h)

h + (x - (x+h))/x(x+h)

h + -h/x(x+h)

Now dividing by the denominator, h

1 + 1/(x²+hx)

Taking the limit

1 + 1/x²

Answer 2

The derivative of the first term is 1 and the derivative of second term is-x^-2.

 

You can do it by taking limit of difference quotient, if that's what you mean by first principle, but I am not going to type that!

typo fixed.