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Derivative of e^(sin²x) with respect to cos x is :
If y = (tan⁻¹x)², show that (x² + 1)² d²y/dx² + 2x(x² + 1) dy/dx = 2.
If y = (sin⁻¹ x)², then find (1 – x²) d²y/dx² – x dy/dx.
The equation of the path traced by a roller-coaster is given by the polynomial f(x) = a(x + 9)(x + 1)(x − 3). If the roller-coaster crosses y-axis at a point (0, −1), answer the following :
If y = √(ax + b), prove that y(d²y/dx²) + (dy/dx)² = 0.
If f(x) = {ax + b ; 0 < x ≤ 1, 2x² - x ; 1 < x < 2} is a differentiable function in (0, 2), then find the values of a and b.
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