How can i derive step response in terms of impulse response from the convolution sum?

1. How do you convert impulse response to step response?
2. Is the impulse response the derivative of the step response?

How do you convert impulse response to step response?

S = impulse2step( I , dt ) converts an impulse response I to a step response S , given the uniform sample interval dt .

Is the impulse response the derivative of the step response?

The step response is the integral with respect to time of the impulse response, and the impulse response is the derivative with respect to time of the step response.