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First, notice that 1/(x^2) = x^(-2)dy/dx = d/dx (x^(-2) + 4x)The derivative of the sum is the sum of the derivatives= d/dx (x^(-2)) + d/dx (4x)The derivative of x^n is nx^(n-1), for every real number n, a...

First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is eq...