# How to Find Differentials in Calculus Quadratics

Quadratic functions are of the form ax^2 + bx + c, where "a," "b" and "c" are positive or negative constants and "x" is the independent variable. The plot of a quadratic function is a parabola. Differential calculus involves finding derivatives of functions. The derivative of a quadratic function, f(x), at any point on a graphical plot is the slope of the tangent line at that point. The derivative is also the rate of change of the function, f(x), with respect to the independent variable, "x." Finding the calculus differential of a quadratic function is relatively simple.

## Instructions

• 1

Verify that the function is a quadratic function. For example, f(x) = 4x^2 + 2x + 1 is a quadratic function because it is of the form ax^2 + bx + c.

• 2

Find the derivative of the x^2 term. In the example, using the power and constant multiple rules of differential calculus, the derivative of 4x^2 is 8x.

• 3

Get the derivative of the "x" term. Again, using the power and constant multiple rules, the derivative of 2x is 2.

• 4

Note that the derivative of a constant term is zero, according to the constant rule of differential calculus.

• 5

Combine the derivatives of the individual terms to find the derivative of the quadratic function. To conclude the example, the derivative of the quadratic function, 4x^2 + 2x + 1, is 8x + 2.

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