If ax² + 2hxy + by² + 2gx + 2fy + c = 0 then find \(\frac{dy}{dx}\).

Find \(\frac{dy}{dx}\) at (1, 1) to the curve 2x² + 3xy + 5y² = 10.

Differentiate the following with respect to x.
(i) x^x
(ii) (log x)^{cos x}

Find the second order derivative of the following functions with respect to x, 3 cos x + 4 sin x

Find the second order derivative of the following functions with respect to x, x sin x