CA Foundation | Quantitative Aptitude | Calculus | Exercise 8 A | ICAI Module Solutions

CA Foundation Chapter - 8 : BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS (Exercise A, Chapter 8 - ICAI Study material)

This video explains the solution of all the problems of Exercise A of Basic Concepts of Differential and Integral Calculus (Chapter 8 in CA Foundation Quantitative Aptitude study material book provided by ICAI).

Click the time stamp to jump to the required question's solution, or watch it all :-

00:00 Intro
00:06 Question 1 - What is the gradient of the curve y=2x^3 - 3x^2 - 12x + 8 at x = 0 ?
01:34 Question 2 - What is the gradient of the curve y = 2x^3 - 5x^2 - 3x at x = 0 ?
02:54 Question 3 - What is the derivative of y = sqrt(x + 1) ?
04:05 Question 4 - What is f'(x) if f(x) = e^(ax^2 + bx + c) ?
05:42 Question 5 - What is f'(x) of (x^2 + 1)/(x^2 - 1) ?
08:00 Question 6 - What is dy/dx if y = x(x - 1)(x - 2) ?
09:29 Question 7 - What is y^2 + dy/dx if xy = 1 ?
10:35 Question 8 - What is the derivative of the function sqrt(x + (sqrt x)) ?
11:50 Question 9 - What is dy/dx if e^(-xy) - 4 xy = 0 ?
14:45 Question 10 - What is dy/dx if x^2/a^2 - y^2/a^2 = 1 ?
15:56 Question 11 - What is dy/dx if log(x/y) = x + y ?
18:11 Question 12 - What is dy/dx if (x, y) = x^3 + y^3 - 3axy = 0?
20:14 Question 13 - What is dy/dx if x = at^2, y = 2at ?
20:42 Question 14 - What is dy/dx if x = 2t + 5, y = t^2 - 2 ?
22:58 Question 15 - What is dy/dx if y = 1/sqrt(x) ?
24:27 Question 16 - What is dy/dx if x = 3t^2 - 1, y = t^3 - t ?
25:49 Question 17 - What is the value of dy/dx at (0, 0) for the curve x^2 + y^2 + 2gx + 2hy ?
28:07 Question 18 - What is dy/dx if (e^3x - e^2x) / (e^3x + e^2x) ?
30:52 Question 19 - What is the value of dy/dx at t = 2 given that x = t + t^-1 and y = t - t^-1 ?
33:04 Question 20 - What is dy/dx at x = 1, y = 1 if x^3 - 2x^2y^2 + 5x + y - 5 = 0 ?
36:47 Question 21 - What is the derivative of x^2(log x) ?
37:55 Question 22 - What is the derivative of (3 - 5x) / (3 + 5x) ?
40:53 Question 23 - What is dy/dx if y = sqrt(2x) + 3^2x ?
42:51 Question 24 - What is the derivative of e^(3x^2 - 6x + 2) ?
44:51 Question 25 - What is the derivative of y = (e^x + 1) / (e^x - 1) ?
47:00 Question 26 - What is dy/dx at t = 2 if x = at^2, y = 2at ?
48:36 Question 27 - What is f'(x) if f(x) = (sqrt(x) + 1/sqrt(x))^2 ?
50:17 Question 28 - What is f'(5) - f'(8) if f(x) = x^2 - 6x + 8 ?
52:38 Question 29 - What is the value of k if f(x) = x^k and f'(1) = 10 ?
53:43 Question 30 - What is dy/dx - sqrt(y^2 - 4) if y = e^x + e^-x ?
57:00 Question 31 - What is the derivative of (x^2 - 1)/x ?
57:57 Question 32 - What is the differential coefficients of (x^2 + 1) ?
58:58 Question 33 - What is dy/dx if y = e^sqrt(2x) ?
1:00:40 Question 34 - What is dy/dx at t = 1 if x = (1 - t^2)/(1 + t^2) and y = 2t/(1 + t^2) ?
1:05:06 Question 35 - What is f'(1) if f(x) = x^2/e^x ?
1:06:44 End Screen

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