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# NCERT Solutions for Class 12 Maths Chapter 6

## NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

The NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives. Which is a part of the Class 12 Math CBSE Syllabus for the academic year 2024-25. The Memorysclub provided for this chapter offers comprehensive explanations and step-by-step solutions to all the questions and exercises. These solutions are provided by subject experts in a well-structured manner, making it easier for students to learn and understand.

## NCERT Solutions for Class 12 Maths Chapter 6 All Exercises

## Important Formula for Chapter 6 Class 12 Maths

In the context of the application of derivatives, some important formulas include:

Derivative Definitions:

- Definition of the derivative: ${\ufffd}^{\mathrm{\prime}}(\ufffd)={\mathrm{lim}}_{\u210e\to 0}\frac{\ufffd(\ufffd+\u210e)-\ufffd(\ufffd)}{\u210e}$
- Power Rule: $({\ufffd}^{\ufffd}{)}^{\mathrm{\prime}}=\ufffd\cdot {\ufffd}^{\ufffd-1}$

Rules for Differentiation:

- Sum Rule: $(\ufffd+\ufffd{)}^{\mathrm{\prime}}={\ufffd}^{\mathrm{\prime}}+{\ufffd}^{\mathrm{\prime}}$
- Product Rule: $(\ufffd\cdot \ufffd{)}^{\mathrm{\prime}}={\ufffd}^{\mathrm{\prime}}\ufffd+\ufffd{\ufffd}^{\mathrm{\prime}}$
- Quotient Rule: ${\left(\frac{\ufffd}{\ufffd}\right)}^{\mathrm{\prime}}=\frac{{\ufffd}^{\mathrm{\prime}}\ufffd-\ufffd{\ufffd}^{\mathrm{\prime}}}{{\ufffd}^{2}}$
- Chain Rule: $(\ufffd\circ \ufffd{)}^{\mathrm{\prime}}={\ufffd}^{\mathrm{\prime}}(\ufffd)\cdot {\ufffd}^{\mathrm{\prime}}$

Applications:

- Rate of change: $\frac{\ufffd\ufffd}{\ufffd\ufffd}$ represents the rate at which $\ufffd$ is changing with respect to $\ufffd$.
- Marginal cost, revenue, and profit: If $\ufffd(\ufffd)$, $\ufffd(\ufffd)$, and $\ufffd(\ufffd)$ are the cost, revenue, and profit functions, then ${\ufffd}^{\mathrm{\prime}}(\ufffd)$, ${\ufffd}^{\mathrm{\prime}}(\ufffd)$, and ${\ufffd}^{\mathrm{\prime}}(\ufffd)$ represent their respective marginal values.

Optimization:

- Critical Points: ${\ufffd}^{\mathrm{\prime}}(\ufffd)=0$ or ${\ufffd}^{\mathrm{\prime}}(\ufffd)$ does not exist.
- Second Derivative Test: ${\ufffd}^{\mathrm{\prime}\mathrm{\prime}}(\ufffd)>0$ implies a local minimum, ${\ufffd}^{\mathrm{\prime}\mathrm{\prime}}(\ufffd)<0$