Differentiability is a part taught in calculus which is a branch of higher mathematics. Differentiability is used to check whether a function is differentiable or not. It consists of one variable function whose derivative exists at each point in its specialisation. In simple words, the graph of a differential function has a non-vertical tangent line at each interior point in its domain. Furthermore, a differential function is considered smooth, which means the function is locally well approximated as a linear function at each interior point and does not contain any break, angle or cusp.
Generally, for x0 as an interior point in the domain of a function f(x), f(x) can be differentiable at x0 only if the derivative f'x0 exists, which means the graph of f(x) has a non-vertical tangent line at the point x0, fx0. Here, the function of f(x) is also called locally linear at x0 (as a linear function near this point well approximates it).
In RD Sharma Solutions for Class 12th Maths Chapter 10 differentiability, students study the differentiability at a point. In this, they solve various exercise problems to get familiarised with the topic. The problems and solutions are given so that it helps students prepare for their board exams.
A topic called differentiability in a set is discussed. In this topic, students are taught how to identify and solve problems based on set differentiability. Using the solutions provided by our experts available at the Aakash website, students can easily understand the concept and enhance their skills by solving the practice problems.
Apart from all these, some useful results on differentiability are studied in the chapter.