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Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these?
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Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)no...
Given Equation:
The given equation is e^-mn - 4xy = 0.
To find dy/dx:
We need to find the derivative of y with respect to x, which can be written as dy/dx.
Approach:
To find dy/dx, we can use implicit differentiation. This means that we differentiate both sides of the equation with respect to x, treating y as a function of x.
Step 1: Differentiate both sides of the equation with respect to x.
Using the chain rule, the derivative of e^-mn with respect to x is (-mn)e^-mn * (dy/dx). The derivative of 4xy with respect to x is 4y + 4x(dy/dx).
Step 2: Simplify the equation.
After differentiating both sides of the equation, we have:
(-mn)e^-mn * (dy/dx) + 4y + 4x(dy/dx) = 0.
Step 3: Solve for dy/dx.
Rearranging the equation, we can isolate dy/dx:
(-mn)e^-mn * (dy/dx) + 4x(dy/dx) = -4y.
(dy/dx)[(-mn)e^-mn + 4x] = -4y.
dy/dx = -4y / [(-mn)e^-mn + 4x].
Final Answer:
Therefore, the derivative dy/dx is given by -4y / [(-mn)e^-mn + 4x].
Option:
The answer is d) none of these
The given equation is e^-mn - 4xy = 0.
To find dy/dx:
We need to find the derivative of y with respect to x, which can be written as dy/dx.
Approach:
To find dy/dx, we can use implicit differentiation. This means that we differentiate both sides of the equation with respect to x, treating y as a function of x.
Step 1: Differentiate both sides of the equation with respect to x.
Using the chain rule, the derivative of e^-mn with respect to x is (-mn)e^-mn * (dy/dx). The derivative of 4xy with respect to x is 4y + 4x(dy/dx).
Step 2: Simplify the equation.
After differentiating both sides of the equation, we have:
(-mn)e^-mn * (dy/dx) + 4y + 4x(dy/dx) = 0.
Step 3: Solve for dy/dx.
Rearranging the equation, we can isolate dy/dx:
(-mn)e^-mn * (dy/dx) + 4x(dy/dx) = -4y.
(dy/dx)[(-mn)e^-mn + 4x] = -4y.
dy/dx = -4y / [(-mn)e^-mn + 4x].
Final Answer:
Therefore, the derivative dy/dx is given by -4y / [(-mn)e^-mn + 4x].
Option:
The answer is d) none of these
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Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these?
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Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these?.
Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given e^-mn - 4xy=0 ,dy/DX can be proved to be a)-y/x b)y/x c)x/y d)none of these?.
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