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If x=e^tan^-1 y-x^2/x^2. find dy/dx.
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If x=e^tan^-1 y-x^2/x^2. find dy/dx.
Given Function:
x = e^(tan^(-1)y) - x^2/x^2
Find dy/dx:
Step 1: Differentiate x with respect to y
dx/dy = d/dy (e^(tan^(-1)y) - x^2/x^2)
Step 2: Apply chain rule to differentiate e^(tan^(-1)y)
dx/dy = d/dy (e^(tan^(-1)y)) - d/dy (x^2/x^2)
Step 3: Differentiate e^(tan^(-1)y) using chain rule
dx/dy = e^(tan^(-1)y) * d/dy (tan^(-1)y) - 2x/x^3
Step 4: Differentiate tan^(-1)y
dx/dy = e^(tan^(-1)y) * (1/(1+y^2)) - 2/x^3
Step 5: Simplify the expression
dx/dy = e^(tan^(-1)y)/(1+y^2) - 2/x^3
Step 6: Find dy/dx using the reciprocal of dx/dy
dy/dx = 1/(dx/dy)
Therefore, dy/dx = 1 / (e^(tan^(-1)y)/(1+y^2) - 2/x^3)
x = e^(tan^(-1)y) - x^2/x^2
Find dy/dx:
Step 1: Differentiate x with respect to y
dx/dy = d/dy (e^(tan^(-1)y) - x^2/x^2)
Step 2: Apply chain rule to differentiate e^(tan^(-1)y)
dx/dy = d/dy (e^(tan^(-1)y)) - d/dy (x^2/x^2)
Step 3: Differentiate e^(tan^(-1)y) using chain rule
dx/dy = e^(tan^(-1)y) * d/dy (tan^(-1)y) - 2x/x^3
Step 4: Differentiate tan^(-1)y
dx/dy = e^(tan^(-1)y) * (1/(1+y^2)) - 2/x^3
Step 5: Simplify the expression
dx/dy = e^(tan^(-1)y)/(1+y^2) - 2/x^3
Step 6: Find dy/dx using the reciprocal of dx/dy
dy/dx = 1/(dx/dy)
Therefore, dy/dx = 1 / (e^(tan^(-1)y)/(1+y^2) - 2/x^3)
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If x=e^tan^-1 y-x^2/x^2. find dy/dx.
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If x=e^tan^-1 y-x^2/x^2. find dy/dx. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x=e^tan^-1 y-x^2/x^2. find dy/dx. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x=e^tan^-1 y-x^2/x^2. find dy/dx..
If x=e^tan^-1 y-x^2/x^2. find dy/dx. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x=e^tan^-1 y-x^2/x^2. find dy/dx. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x=e^tan^-1 y-x^2/x^2. find dy/dx..
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