# 2.2 Definition Of Derivativeap Calculus

Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.

Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. In this chapter, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. From this very brief informal look at one limit, let’s start to develop an intuitive definition of the limit.We can think of the limit of a function at a number latexa/latex as being the one real number latexL/latex that the functional values approach as the latexx/latex-values approach latexa/latex, provided such a real number latexL/latex exists.

Here are few online resource, which are very helpful to find derivative.

## 2.2 Definition Of Derivativeap Calculus Algebra

### Contents and summary

- Geometrical interpretation of the derivative
- Marginal functions in economics
- Inverse trigonometric functions
- Derivative of hyperbolic functions
- Logarithmic Differentiation
- Newtorn Raphson Method
- Some standard nth derivatives
- Functions of several variables
- Limit and continuity
- Differentiability

### Solutions

- Exercise 2.2 View online Download PDF

- Exercise 2.4 View online Download PDF

- Exercise 2.6 View online Download PDF

### Notes by Prof M. Tanveer

## 2.2 Definition Of Derivativeap Calculus Solver

- Exercise 2.2 View Online Download PDF

## 2.2 Definition Of Derivativeap Calculus 14th Edition

- Exercise 2.5 View Online Download PDF

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2.2 Version 2 Answers

## 2.2 Definition Of Derivativeap Calculus Calculator

1. A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage of full capacity that the battery reaches as a function of time t elapsed (in hours).

2. Let f(x) = x^3

3. Find the derivative of the function using the definition of the derivative. f(x) = 1x/2 – 1/10

4. Find the derivative of the function using the definition of the derivative.

F(x) = 7.5x^2 – x + 2.8

5. Find the derivative of the function using the definition of the derivative.

G(t) = 3/t^1/2

6. Find the derivative of the function using the definition of the derivative.

g(x) = sqrt(5 – x)

8.The graph of f is given. State the numbers at which f is not differentiable.

9. The graph of f is given. State the numbers at which f is not differentiable.

10. Use the definition of the derivative to find f’(x) and f’’(x).

f(x) = 4x^2 + 3x + 3

11. If f(x) = 2x^2 – x^3, find f’(x), f’’(x), f’’’(x), and f(4)(x).

12. If f(t) = t^1/3 and a cannot = 0, find f’(a).