1.

Find the derivative of the following functions 'ab initio', that is, using the definition.x^2+1

Answer»

SOLUTION :LET `y=x^2+1`
Then `dy/dx=lim_(deltaxto0)([(x+DELTAX)^2+1]-[x^2+1])/(deltax)`
`=lim_(deltaxto0)(x^2+2xcdot deltax+deltax^2-x^2)/(deltax)`
`=lim_(deltaxto0)(2X+deltax)=2x`


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