Well, grad f(r) is (df(r)/dx, df(r)/dy, df(r)/dz). However, r is sqrt(x^2 + y^2 + z^2). Use the chain rule so that the terms look like df/dr * dr/dx, then take out the common factor of df/dr. Finally, evaluate what's left by putting r = sqrt(x^2 + y^2 + z^2) and rewriting the whole thing in terms of r.
Actually f is the function of r. And when the variables of a vector is not mentioned we use the generalized variables, i.e., (x,y,z) {the cartisian coordinates}.