NCERT

Class 12 Applications of Derivatives chapter focuses on using derivatives and its concepts to solve real-life problems like rate of change, maxima and minima, increasing/decreasing functions, and finding tangents/normals of the curves at any given co-ordinates. Application of Derivatives is one of the most essential chapter for overall understanding of class 12th calculus unit. 

Continuity and Differentiability is one of the most important chapters for CBSE Class 12 Maths board exams. Continuity and Differentiability carries significant weightage of around 6-8 marks in the class 12 board exams. Students can use our Class 12 Math Continuity and Differentiability NCERT Solutions for their benefits, to better preparation and conceptual clarity. students can secure good marks from this chapter by clearing the basics with the help of out NCER Solution prepared by experts in Shiksha.

There are several important formulas of the Continuity and Differentiability, Students can cheeck below;

1. Continuity at a point
   $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)$limx?a?f(x)=limx?a+?f(x)=f(a)

2. Derivative of basic functions:

   • $\frac{d}{dx}(x^n) = nx^{n-1}$dxd?(xn)=nxn?1

   • $\frac{d}{dx}(\sin x) = \cos x$dxd?(sinx)=cosx

   • $\frac{d}{dx}(\cos x) = -\sin x$dxd?(cosx)=?sinx

   • $\frac{d}{dx}(e^x) = e^x$dxd?(ex)=ex

   • $\frac{d}{dx}(\ln x) = \frac{1}{x}$dxd?(lnx)=x1?

3. Product Rule:
   $\frac{d}{dx}[u \cdot v] = u \cdot \frac{dv}{dx} + v \cdot \frac{du}{dx}$dxd?[u?v]=u?dxdv?+v?dxdu?

4. Quotient Rule:
   $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2}$dxd?(vu?)=v2v?dxdu?u?dxdv?

5. Chain Rule:
   If $y = f(g(x))$y=f(g(x)), then
   $\frac{dy}{dx} = f'(g(x)) \cdot g'(x)$dxdy?=f?(g(x))?g?(x)

Students can check our Shiksha's NCERT Solutions Page for more information.

The concept of continuity is defined for a function  as a curve that is smooth and unbroken at every point in its domain. Mathematically, a function $f (x)$ is said to be continuous at a point $x = a$ if:

$\lim_ {x \to a} f (x) = f (a)$

What it means:

• The function is defined at $x = a$,

• The limit of the function exists as $x$ approaches $a$,

• And the limit is equal to the function's value at that point.

Students can check the NCERT Class 12 Maths Chapter 5 Continuity and Differentiability for better and deep understanding of the topic.

Yes, Shiksha's NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability are aligned with the latest CBSE 2025 syllabus. Our NCERT Solutions are prepared by subject experts to provide step-by-step explanations, aiding students in their preparation for their board exams. Student can access these solutions and even download the PDF for free on our website Shiksha.

Students can find well structured NCERT Solutions for Class 12 Continuity and Differentiability in PDF form. We have provided the Solution PDF for all the chapters on our pages, in the Download Free PDF Section. Students can use these NCERT Solutions PDF for their offline study, and as a good and handy resource for practice and revision.

NCERT Class 12 Maths includes Continuity and Differentiability as Chapter 6, which is one of the fundamental concepts in calculus.

• Continuity is defined for a function in a way that curve of function behaves smoothly without any breaks or jumps at a point or over an interval.
• Differentiability deal with whether a function has a defined derivative at a point, meaning it has a clear slope or tangent. 

Students can check our NCERT solutions for Continuity and Differentiability for better understanding.

Yes, We have updated our NCERT Class 12 Maths Relations and Functions solutions updated as per the latest CBSE 2025 syllabus.We have designed to provide best method of problem-solving which ensures better scoring capabilty of students.These updated solutions help students to do self-preparation, and give confidence while solving board exam questions.

Students can find accurate NCERT Solutions for Class 12 Maths Relations and Functions on our website Shiksha.com. We provide step-by-step explanations that are easy to understand and follow the latest CBSE 2025 syllabus and exam pattern. Whether Students are preparing for board exams orfor Compeptive exams, these solutions help build a strong conceptual understanding.

Students can download the free Class 11 Limits and Derivatives NCERT Solutions PDF from our website Shiksha, which offers chapter-wise and exercise-wise solutions. These PDFs are available for free and students can access  and download it to use it offline. Studernts can access the PDF directly on the Limits and Derivatives NCERT Solutions page provided by Shiksha as a part of class 11 chapter-wise matgh solutions.