1.

Find the derivative of the following functions 'ab initio', that is, using the definition.1/x

Answer»

SOLUTION :LET y=1/x
Then `dy/dx=lim_(deltaxto0)(1/(x+deltax)-1/x)/(deltax)`
`=lim_(deltaxto0)(x-(x+deltax))/(x(x+deltax)cdotdelta x)`
`=lim_(deltaxto0)1/(x(x+deltax))=-1/x^2`


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