Limit Definition Of A Derivative

The derivative of a function represents its rate of change at any given point. In this case, the function is x^2. To find its derivative, we can apply the power rule of differentiation. According to the power rule, when we differentiate x^n, the result is n*x^(n-1). Applying this rule to x^2, we get 2*x^(2-1), which simplifies to 2x. Therefore, the derivative of x^2 is 2x.

The derivative of a function represents the rate of change of the function at a given point. To find the derivative of x^4+3, we can apply the power rule, which states that the derivative of x^n is equal to n*x^(n-1). Applying this rule, the derivative of x^4 is 4*x^(4-1) = 4*x^3. Since we are interested in finding the derivative at x=2, we substitute x=2 into the derivative expression: 4*2^3 = 4*8 = 32. Therefore, the derivative of x^4+3 at x=2 is 32.