Derivatives...finding a general formula for f^n (x)

Question

Find a general formula for f⁽ⁿ⁾ (x) . 

 

f(x)=x²e^x 

 

Ive tried understanding how to do this from my book, and I just dont get it. This is the only question im having trouble with. I know how to do derivatives but I have no idea what is meant by this general formula thing. Please show me steps.n

Answer 1

the notation (n) "upstairs" from f means n^th derivative.

 

So take the first derivative f' and then the second derivative f" and then the third derivative f'''(x) which can also be notated as f⁽³⁾(x).

 

Examine these and you can INFER the answer.

 

DO NOT OMIT THE PARENTHESES AROUND THE DERIVATIVE NUMBER (as you did in your title).