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Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0?
Most Upvoted Answer
Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0?
Actually it should be (1+x^2)^2
and then all gets simple...
just differentiate it once and then twice and put the values in and you'll get the answer...
and then all gets simple...
just differentiate it once and then twice and put the values in and you'll get the answer...
Community Answer
Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0?
Proof:
Given: Y = e^(tan^(-1)X)
Step 1: Find the first and second derivatives of Y with respect to X.
Y = e^(tan^(-1)X)
Taking natural logarithm on both sides:
ln(Y) = tan^(-1)X
Differentiating both sides with respect to X:
(1/Y) * dY/dX = 1/(1+X^2)
dY/dX = Y/(1+X^2)
Now, differentiate dY/dX with respect to X:
d^2Y/dX^2 = (dY/dX) * (-2X/(1+X^2)^2)
d^2Y/dX^2 = -2X * Y/(1+X^2)^2
Step 2: Substitute the derivatives into the given expression.
(1+X^2) * d^2Y/dX^2 * (2X-1) * dY/dX
= (1+X^2) * (-2X * Y/(1+X^2)^2) * (2X-1) * Y/(1+X^2)
= -2X * Y * (2X-1) * Y/(1+X^2)
= -2X(2X-1) * Y^2/(1+X^2)
= -4X^2Y^2 + 2XY^2
Step 3: Simplify the expression.
Since Y = e^(tan^(-1)X), we can substitute this into the expression:
-4X^2(e^(tan^(-1)X))^2 + 2Xe^(tan^(-1)X)
= -4X^2(e^(2(tan^(-1)X))) + 2Xe^(tan^(-1)X)
= -4X^2(e^(tan^(-1)(X))^2) + 2Xe^(tan^(-1)X)
= 0
Therefore, (1+X^2)d^2Y/dX^2 * (2X-1) * dY/dX = 0.
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Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0?.
Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Y=e^tan(inverse)X,prove that (1+ X²)d2y/dx2 (2x-1) dy/dX=0?.
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