If y = f(x) = x^(p/q) then y^p = x^p
show through implicit differentiation that
d/dx[x^(p/q)] = (p/q)x^[p/q]
Not sure how to tackle this problem.
start with y^p = x^p, it should be y^q = x^p
q(y^(q-1) dy/dx = p(x^(p-1)
dy/dx = p(x^(p-1)) / (q(y^(q-1))
= [p(x^p)/x] / [q(y^q)/y] , remember y = x^(p/q)
= (p/q)(x^p)/(x^p)(y/x)
= (p/q)(y/x)
= (p/q)(x^(p/q) / x
check my works, I have that extra x hanging around