In the above difference quotient, all the variables except x are held fixed.

This property can be generalized to all difference quotients.

This is where the difference quotient comes in.

We will show that the difference quotient for f g is always equal to:

The process of finding the derivative via the difference quotient is called differentiation.

If a finite difference is divided by b a, one gets a difference quotient.

In short, the definition is made more restrictive by allowing both points used in the difference quotient to "move".

The difference quotient, however, allows you to find the slope of any curve or line at any single point.

The expression on the left side of the equation is Newton's difference quotient for F at x.

The derivative is the value of the difference quotient as the secant lines approach the tangent line.

This expression is called a difference quotient.

However, the usual difference quotient does not make sense in higher dimensions because it is not usually possible to divide vectors.

After we find the difference quotient of a function, we have a new function, called the derivative.

The last term is the difference quotient (the slope of the secant line), and taking the limit yields the derivative.

In many cases, complicated limit calculations by direct application of Newton's difference quotient can be avoided using differentiation rules.

The definition of strict differentiability avoids this problem by imposing a condition directly on the difference quotients.

In calculus, an advanced branch of mathematics, the difference quotient is the formula used for finding the derivative.

Instead, define Q(h) to be the difference quotient as a function of h:

Consequently the secant lines do not approach any single slope, so the limit of the difference quotient does not exist.

The derivative of a function can, in principle, be computed from the definition by considering the difference quotient, and computing its limit.

The derivative is the rate at which a function changes, and the derivative is based on the difference quotient.

The difference quotient was formulated by Isaac Newton.

The expression on the right can be written as a difference quotient of difference quotients:

The first derivative of the delta function is the distributional limit of the difference quotients:

The difference quotient becomes: