Ncert Solutions Maths class 12th

Students must understand that a complete understanding of the topic can only come through solving all types of questions of the chapter in other words practice all exercises of the chapter. All exercises cover different types and levels of problems, including general and particular solutions, variables separable, and linear equations. We recommend our readers to take help of our Class 12 NCERT Solutions for Differential Equations while solving all the exercises to clear doubts, understand conceptual references and using formuals whenever neccessary.

We all are aware that all the quesstions asked in the CBSE Class 12 Board Exams are based on NCERT Textbooks. This information tells that if students only cover whole NCERT textbook it will enough for the boards. Shiksha's NCERT Solutions are more than sufficient for CBSE Board Exams as they cover all textbook problems and provide accurate and step-by-step explanation of the questions. 

Differential Equations include various important topics which are important for class 12 boards as well as competitve exams. There are several important topics including order and degree of differential equations, general and particular solutions, variables separable method, homogeneous equations, and linear differential equations. Questions related to these topics are frequently asked in CBSE board exams.

While preparing the Shiksha's NCERT Solutions for Applications of Derivatives, our experts have focused to make them easy to understand, complete, and crysatal clear concptual resource. Our NCERT Solutions provide simple and step-by-step explanations of the quesrtions of the exerrcise. 

Students can tak ehelp of our Solutions to understand topics like increasing/decreasing functions, tangents, normals, and maxima/minima with clarity. Shikhsa's NCERT solutions strictly follow the latest CBSE  2025 syllabus, making them ideal for board exam preparation as well as for basic competitive exam prep.

Students should use our NCERT Applications of Derivatives Solutions to begin their JEE preparation as a resource to build strong foundation.  Our solutions follow the lates CBSE Class 12 syllabus which make them a complete resource for CBSE Boards prepaation, Yet for competitive exam like JEE, Student must go beyond NCERT and refer to advanced-level books like arihant, cengage or coaching material availble to them.

? Shiksha's NCERT Solutions for Class 12 Applications of Derivatives are designed to serve a holistic mathematical guide for the chapter for all students. That's whay our solutions focus on providing step-by-step textual explanations for each exercise as well as visual representation on 2D graphs along with solutions for better understanding .

We help students with all kinds of problems including those involving increasing/decreasing functions, tangents, normals, and maxima/minima, there is graphical method explanations attached whenever neccessary in image form in the solutions.?

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.

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.