Determine dy/dx given that 5^y^2 = 2xtany. Solution We have to differentiate 5^(y^2) = 2x*tan y with respect to x. Use implicit differentiation on both the sides. => `2*ln 5*y*5^(y^2)*(dy/dx) = 2*tan y + 2x*sec^2y*(dy/dx)` => `dy/dx = (2*tan y)/(2*ln 5*y*5^(y^2) - 2*x*sec^2 y)` The required derivative `dy/dx = (2*tany)/(2*ln 5*y*5^(y^2) - 2x*sec^2 y)`.