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If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these?
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If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e....
Solution:
Given, y= 2(x 3) (4/logx 3)
We need to find dy/dx.
Using the product rule, we get:
dy/dx = 2(x 3) d/dx (4/logx 3) + (d/dx (2(x 3))) (4/logx 3)
Let's find each derivative separately.
d/dx (4/logx 3)
Using the chain rule, we get:
d/dx (4/logx 3) = 4 d/dx (ln 3)/d/dx (ln x)
= 4 (1/3) (1/x) = 4/(3x)
(d/dx (2(x 3)))
Using the power rule, we get:
d/dx (2(x 3)) = 2 d/dx (x 3)
= 2 (x 2)
Substituting these values in the expression for dy/dx, we get:
dy/dx = 2(x 3) (4/(3x)) + 2(x 2) (4/logx 3)
= 8(x 2)/(logx 3) - 8/(3x)
= 8(2x)/(log2 (x)) - 8/(3x)
= 8(2/x) log2 (x) - 8/(3x)
Therefore, the correct option is (a) 8.2 x log 2 (4/x) log3 e.
Note: The answer has been broken into headings and HTML bullet points to make it more organized and readable.
Given, y= 2(x 3) (4/logx 3)
We need to find dy/dx.
Using the product rule, we get:
dy/dx = 2(x 3) d/dx (4/logx 3) + (d/dx (2(x 3))) (4/logx 3)
Let's find each derivative separately.
d/dx (4/logx 3)
Using the chain rule, we get:
d/dx (4/logx 3) = 4 d/dx (ln 3)/d/dx (ln x)
= 4 (1/3) (1/x) = 4/(3x)
(d/dx (2(x 3)))
Using the power rule, we get:
d/dx (2(x 3)) = 2 d/dx (x 3)
= 2 (x 2)
Substituting these values in the expression for dy/dx, we get:
dy/dx = 2(x 3) (4/(3x)) + 2(x 2) (4/logx 3)
= 8(x 2)/(logx 3) - 8/(3x)
= 8(2x)/(log2 (x)) - 8/(3x)
= 8(2/x) log2 (x) - 8/(3x)
Therefore, the correct option is (a) 8.2 x log 2 (4/x) log3 e.
Note: The answer has been broken into headings and HTML bullet points to make it more organized and readable.
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If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these?
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If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these?.
If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y= 2(x 3) (4/logx 3), then dy/dx is : a. 8.2 x log 2 (4/x) log3 e. b. 8.2 x (4/x) log3 e. c. 2 x-2 log 2 (4/x) log3 e. d. None of these?.
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