carlarae said:I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?
A differentiable function of x is a mathematical function that is continuous and smooth, with no abrupt changes or discontinuities. This means that the function has a well-defined derivative at every point within its domain.
A function is differentiable at a specific point if the limit of the difference quotient (slope of the tangent line) exists at that point. This means that the function must be continuous and have a well-defined derivative at that point.
A differentiable function is continuous and has a well-defined derivative at every point within its domain. A non-differentiable function, on the other hand, may have abrupt changes or discontinuities, making it not smooth and not having a well-defined derivative at certain points.
No, a function cannot be differentiable but not continuous. Differentiability implies continuity, as a function must be continuous for the limit of the difference quotient to exist at every point within its domain.
Differentiable functions are important in mathematics and science because they allow us to model and analyze real-world phenomena. They also play a crucial role in calculus, as the derivative of a function is used to find the rate of change, critical points, and optimization in various applications.