Mathematica Labs | Denis Shubleka

Subject: Calculus

Topic: Higher Order Derivatives

Goal: Use Mathematica to compute higher order derivatives.

Task 1

Let’s define a function f(x) and compute its second deriative, using
two single quotation marks.

f[x_]:=Cos[(x^3)];
f''[x]

Three quotation marks are used for the third derivative of f(x). Try it:

f'''[x]

The command D[f(x),{x,degree}] can also be used to compute higher order 
derivatives. The following finds the fifth derivative of the 
given function:

D[f[x],{x,5}]

To find the fifth derivative and evaluate it at x=3, we use:

D[f[x],{x,5}]/.x->3

Your turn: find the 50th derivative of g(x)=sec x and evaluate at x=1.

Related Exercises/Notes:

ap-calc.github.io