Find the derivative of y=2x²-x using first principle
To find the derivative of y = 2x² - x using first principles, we start with the definition of the derivative:
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
In this case, our function is f(x) = 2x² - x. So we substitute this into the formula:
f'(x) = lim(h->0) [(2(x+h)² - (x+h)) - (2x² - x)] / h
f'(x) = lim(h->0) [(2x² + 4xh + 2h² - x - h) - 2x² + x] / h
f'(x) = lim(h->0) [4xh + 2h² - h] / h
f'(x) = lim(h->0) 4x + 2h - 1
Now we can simplify the expression by letting h approach 0:
f'(x) = 4x - 1
Therefore, the derivative of y = 2x² - x using first principle is f'(x) = 4x - 1.