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

Explanation

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`