1.

Find the derivative of the following functions 'ab initio', that is, using the definition.t(t-1)

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Solution :LET `y=t(t-1)=t^2-t`
Then
`dy/dt=lim_(DELTAT TO0)([(t+deltat)^2-(t-deltat)]-[t^2-t])/(deltat)`
`=lim_(deltat to0)(t^2+2tdeltat+deltat^2-t-deltat-t^2+t)/(deltat)`
`=lim_(deltat to0)[(2t-1)+deltat]=2t-1`


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