### Home > CALC > Chapter Ch10 > Lesson 10.1.7 > Problem 10-66

By now you are comfortable with the graphical implications of the first and second derivatives of a function.

*f*′(*x*) gives you the slope of the tangent while*f*″(*x*) tells you the concavity of the graph at a point. There is nothing to stop us from finding the third and fourth (and beyond!) derivatives, but there are not any significant graphical characteristics associated with higher derivatives.*f*′″(*x*) is simply the rate of change of*f*″(*x*) and so on.Notation: We cannot simply put more and more tic marks for, say, the 7

^{th }derivative. Instead, the 7^{th}derivative of*f*(*x*) is written*f*^{(7)}(*x*), using italicized roman numerals. The*n*^{th}derivative of a function is written*f*^{(}^{n}^{) }(*x*). Homework Help ✎Find

*f*^{(4) }(*x*) for*f*(*x*) =*x*^{8}.If

*f*(*x*) =*e*^{2}^{x}^{ }, find an expression for the*n*^{th}derivative,*f*^{(n) }(*x*).

Take the derivative four times.

Take a few derivatives of this function and look for patterns.