I have to solve this question

Find d^2y/d^2x and d^3y/d^3x if y is defined implicitly by y+sin(y)=x

So far I have 

f:=y+sin(y)=x;

implicitdiff(f,y,x$2);

and

implicitdiff(f,y,x$3);

both of them spit out answers, but am I doing that right for the question that is asked?

On the test I had today I was asked to find the derivative of x^3+3*cos(x) using the definition of a derivative. The (f(x+h)-f(x))/h type.

So i set my function and then used the definition and then tried to simplify. Unfortunately the bottom h is still there so when I try to evaluate the function when h=0 it returns an obvious problem. It can't divide by zero. Usually when I do this the h on the bottom will be canceled out, but it wouldn't do it for this one. Does...