Capitalism is an economic system based on private ownership of the means of production and their operation for profit. Characteristics central to capitalism include private property, capital accumulation, wage labor, voluntary exchange, a price system, and competitive markets.
f(x) = (x+1)^1/2. Hi Carla, The derivative of $f(x)$ is the limit, as $h$ approaches zero of the difference quotient. \[\frac{f(x + h) - f(x)}{h}.\]. For your function this difference quotient is. \[\frac{(x + h + 1)^{1/2} - (x + 1)^{1/2}}{h}.\]. If you multiply the numerator and denominator by $(x + h + 1)^{1/2} + (x + 1)^{1/2}$ and simplify you will arrive at an expression that can be evaluated as $h$ approaches zero.
You can see this clearly if you consider the unit circle, where sin(t) = y, cos(t) = x, and the hypotenuse is 1. sin(t) = sin(t) cos(t) = cos(t) tan(t) = tan(t) Notice in particular that sine and tangent are odd functions, while cosine is an even function. Angle-Sum and -Difference Identities.