tan^{-1} (3x - x^{2}/ 1 - 3x^{2}) dy/dx ज्ञात कीजिए
Answers
dy/dx = (9x² -2x + 3)/(9x⁴ - 7x² + 3x + 1) यदि y = Tan⁻¹((3x - x²)/(1 - 3x²))
Step-by-step explanation:
dy/dx ज्ञात कीजिए
y = Tan⁻¹((3x - x²)/(1 - 3x²))
=> Tany = (3x - x²)/ (1 - 3x²)
=> Sec²y (dy/dx) = ((3x - x²)(-1)/(1 - 3x²)²)(-6x) + (3 - 2x)/(1 - 3x²)
=> (1 + Tan²y)(dy/dx) = (18x² - 6x³)/(1 - 3x²)² + (3 - 2x)/(1 - 3x²)
=> (1 + Tan²y)(dy/dx) = (18x² - 6x³ )/(1 - 3x²)² + (3 - 2x)(1 - 3x²)/(1 - 3x²)²
=> (1 + Tan²y)(dy/dx) = (18x² - 6x³ + 6x³ + 3 - 2x - 9x²)/(1 - 3x²)²
=> (1 + Tan²y)(dy/dx) = (9x² -2x + 3)/(1 - 3x²)²
1 + Tan²y = 1 + ((3x - x²)/ (1 - 3x²))²
=> 1 + Tan²y = (1 + 9x⁴ - 6x² + 3x - x²)/(1 - 3x²)²
=> 1 + Tan²y = (9x⁴ - 7x² + 3x + 1)/(1 - 3x²)²
(9x⁴ - 7x² + 3x + 1)/(1 - 3x²)²(dy/dx) = (9x² -2x + 3)/(1 - 3x²)²
=> dy/dx = (9x² -2x + 3)/(9x⁴ - 7x² + 3x + 1)
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