Find d^2y/dx^2 by implicit differentiation of Square root x + Square root y = 1

Question

Find d^2y/dx^2 by implicit differentiation of Square root x + Square root y = 1 1/2xSquare root x x - y/2x Square root x Square root y Square root x - Square root y/2x Square root x Square root y -y/x None of these Find an equation of the tangent line to the curve x^2 + 2xy - y^2 + x = 2 at (1, 2). y - 2 = 7/2 (x - 1) y - 2 = 5/2 (x - 1) y - 2 = 3/2 (x - 1) y - 2 = 1/2 (x - 1) None of these. Find the derivative of f(x) = (ln x)^4. 1/x^4 4/x^3 4(ln x)^3 4(ln x)^3/x None of these. Find the derivative of f(x) = ln x/x^2 + 1 1 - x^2/x(x^2 + 1) 1 - x^2/(x^2 + 1)^2 x^2 + 1/x

Explanation / Answer

x^2 + 2xy - y^2 +x=2
Differentiate with respect to x,
2x + 2y + 2xdy/dx - 2ydy/dx +1=0
Here dy/dx is slope of tangent

At point(1,2)
2 + 4 + 2dy/dx - 4dy/dx +1=0
7 = 2 dy/dx
dy/dx = 7/2

So, equation of line through (1,2) and slope 7/2 is
(y-2) = 7/2(x-1)
So, A is correct answer.

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