Can some one help to explain this step?
Ignoring the summation because that's in both lines, work the problem from there.
In the top line you're taking the derivative with respective w of
If you focus on the bit in parenthesis we can expand it manually. It's a bit of work, but we'll get:
w^2*x^2 + 2*w*x*b - 2*w*x*t - 2*b*t + t^2 + b^2
So we have, multiplied by 1/2 and with a derivative with respect to w. We'll move the 1/2 out of the way for now because it doesn't affect the derivative, and we'll just take the derivative of that line above. It's a polynomial so we drop any terms that don't have a w, and for any terms that do have a w we lower the order of the exponent on w and multiply term by that exponent. All of the exponents on w are either 1 or 2 so we're left with:
2*w*x^2 + 2*x*b - 2*x*t
Now we have that 1/2 from earlier, which quite nicely cancels out all of the factors of 2:
w*x^2+ x*b - x*t
And lastly, we see that all of the terms have a multiplcation of x, so we can factor that out:
x * (w*x + b - t)
Hopefully going step by step clears that up. The two keys are 1) expanding the parenthesis squared, and 2) knowing the rules derivation (moving the 1/2 and take derivates of w and w^2)