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Is the following system stable. If so how.

y(t)= [itex]\frac{d}{dt}[/itex] x(t)

I have tried the following proof but i think it is wrong.

ie . [itex]\int^{\infty}_{-\infty} h(t) dt[/itex] < [itex]\infty[/itex] --------- 1

For the above system h(t) = [itex] \delta^{'}(t)[/itex]

so on applying h(t) = [itex] \delta^{'}(t)[/itex] in eq. 1

[itex]\int^{\infty}_{-\infty} \delta^{'}(t) dt[/itex] = [itex] \delta(0)[/itex]

So the system is not stable.

I think the above proof is way off the mark.

please provide the correct proof. thanks

y(t)= [itex]\frac{d}{dt}[/itex] x(t)

I have tried the following proof but i think it is wrong.

**PROOF:**- The System is LINEAR
- The system is time invariant

**So on applying the stability criterion for LTI systems**ie . [itex]\int^{\infty}_{-\infty} h(t) dt[/itex] < [itex]\infty[/itex] --------- 1

For the above system h(t) = [itex] \delta^{'}(t)[/itex]

so on applying h(t) = [itex] \delta^{'}(t)[/itex] in eq. 1

[itex]\int^{\infty}_{-\infty} \delta^{'}(t) dt[/itex] = [itex] \delta(0)[/itex]

So the system is not stable.

I think the above proof is way off the mark.

please provide the correct proof. thanks

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