### Derivative of constant and x^n.

 We know the formula for finding the derivative ```dy/dx = lim [f(x + δx) - f(x)]/δx δx→0 ``` Constant function For the constant function f(x) = c where c is a constant and f(x + δx) = c, f(x + δx) - f(x) = 0 So, dy/dx = 0 Derivative of xn For xn, f(x) = xn and f(x + δx) = (x + δx)n f(x + δx) = (x + δx)n By binomial expansion = nC0xn + nC1xn-1δx + nC2xn-2(δx)2 + nC3xn-3(δx)3 + ... = xn + (n/1!) xn-1δx + (n(n-1)/2!) xn-2(δx)2 + (n(n-1)(n-2)/3!) xn-3(δx)3 + ... The difference f(x + δx) - f(x) = xn + (n/1!) xn-1δx + (n(n-1)/2!) xn-2(δx)2 + (n(n-1)(n-2)/3!) xn-3(δx)3 + ... - xn f(x + δx) - f(x) = nxn-1δx + (n(n-1)/2!) xn-2(δx)2 + (n(n-1)(n-2)/3!) xn-3(δx)3 + ... The ratio [f(x + δx) - f(x)]/δx = nxn-1 + (n(n-1)/2!) xn-2δx + (n(n-1)(n-2)/3!) xn-3δx2 + ... As ```dy/dx = lim [f(x + δx) - f(x)]/δx δx→0``` ` ` When δx→0 all the terms containing δx becomes very small and negligible then d(xn)/dx = nxn-1 dc/dx = 0, c is a constant and d(xn)/dx = nxn-1, where n is an integer.