By using implicit differentiation, find dy/dx of sin(x^2/y^2)=x?

Find dy/dx by implicit differentiation. Sinx+10cos3y=2? We want to differentiate both sides of the equation with respects to x... First we want to know the derivative rules: d/dx (sin x) = cos x d/dx (cos x) = -sin x d/dx (f(g(x)) = f'(g(x)) * g'(x) (taking derivative of inner function times derivative of outer function).. d/dx (ax^b) = (a*b)x^(b-1) d/dx (a) = 0 (derivative of constants are 0)... Now differentiate, the left side of each term...apply the chain rule on 10cos(3y) term...and the right side is just 0 since it's just a constant)...so.. d/dx (sin x) + 10 * d/dx (cos (3y)) = d/dx (2) The derivative of sin (x) is cos (x)... The derivative of cos (x) is -sin (x)... cos x + 10 * -sin (3y) * d/dx (3y) = 0 To differentiate 3y...simply apply the power rule for derivatives..

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