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If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2
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If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2
Given: x = a(cosx xsinx), y = a(sinx - xcosx)
To find: d^2 y/dx^2
Solution:
Step 1: Find dy/dx
Given, y = a(sinx - xcosx)
Differentiating both sides w.r.t x, we get
dy/dx = a(cosx - cosx + xsinx) = axsinx
Step 2: Find d^2 y/dx^2
Differentiating dy/dx w.r.t x, we get
d^2 y/dx^2 = a(cosx + cosx + xcosx) = 2acosx + axcosx
Therefore, d^2 y/dx^2 = 2acosx + axcosx is the required second derivative of y w.r.t x.
Final Answer: d^2 y/dx^2 = 2acosx + axcosx
To find: d^2 y/dx^2
Solution:
Step 1: Find dy/dx
Given, y = a(sinx - xcosx)
Differentiating both sides w.r.t x, we get
dy/dx = a(cosx - cosx + xsinx) = axsinx
Step 2: Find d^2 y/dx^2
Differentiating dy/dx w.r.t x, we get
d^2 y/dx^2 = a(cosx + cosx + xcosx) = 2acosx + axcosx
Therefore, d^2 y/dx^2 = 2acosx + axcosx is the required second derivative of y w.r.t x.
Final Answer: d^2 y/dx^2 = 2acosx + axcosx
Community Answer
If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2
Sec^3 x/ax
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If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2
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If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2 for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2 covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2.
If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2 for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2 covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = a(cosx+xsinx), y = a(sinx - xcosx), find d^2 y/dx^2.
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