First, the derivative f'=-3x^-4 or -3/x^4, because f(x)=1/x^3=x^-3, and the usual rule for the derivative applies: d(x^n)=nx^(n-1). So f' is the tangent with the value at (a,f(a)) of -3/a^4. The equation of the tangent line is y=mx+b, the standard linear equation, where m=gradient=tangent=-3/a^4. Putting in the tangent point: f(a)=1/a^3, so 1/a^3=-3a/a^4+b=-3/a^3+b, and b=1/a^3+3/a^3=4/a^3 and a^4y=4a-3x. (dy/dx=-3/a^4 at x=a, same as f').