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If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal to
a)2e^5x
b)1/(e^5x +e^2x)^2
c)e^5x/(e^5x+e^2x)
d)none?
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If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa...
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If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa...
Solution:
Given, y = (e^(3x)-e^(2x))/(e^(3x)e^(2x))

To find dy/dx

Step 1: Simplify y

y = (e^(3x)-e^(2x))/(e^(5x)) [Using exponential laws]

Step 2: Differentiate y with respect to x

Using quotient rule, we get

(dy/dx) = ((e^(5x))(3e^(3x)-2e^(2x)) - (e^(3x)-e^(2x))(5e^(5x)))/(e^(5x))^2

Simplifying the above expression, we get

(dy/dx) = (3e^(3x)-2e^(2x) - 5e^(3x)+5e^(2x))/(e^(5x))

(dy/dx) = (-2e^(3x)+3e^(2x))/(e^(5x))

(dy/dx) = e^(2x)(3-e^x)/(e^(5x)) [Using exponential laws]

(dy/dx) = (3-e^x)/(e^(3x)) [Canceling out e^(2x) from numerator and denominator]

Hence, the correct option is (c) e^(5x)/(e^(5x)e^(2x))
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If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa)2e^5xb)1/(e^5x +e^2x)^2c)e^5x/(e^5x+e^2x)d)none?
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If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa)2e^5xb)1/(e^5x +e^2x)^2c)e^5x/(e^5x+e^2x)d)none? 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=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa)2e^5xb)1/(e^5x +e^2x)^2c)e^5x/(e^5x+e^2x)d)none? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=e^3x-e^2x divided by e^3x+e^2x then dy divided by dx is equal toa)2e^5xb)1/(e^5x +e^2x)^2c)e^5x/(e^5x+e^2x)d)none?.
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