Derivatives Worksheet 3

M408 – Honors Advanced Precalculus Name ________________________
Unit 5 – Derivatives
Worksheet 3 – Derivatives on the TI-89 Teacher ______________________
Part I: Finding the Derivative of a Functions on the TI-89
5 1
Let fx 3x . Recall, the notation for the derivative of f(x) is f x x
d
f x .
dx
To find the derivative of a function on the TI-89,
o Press 2 nd 8 or F3: CALC: 1: d(differentiate)
o Type the expression (…the right side of the
function)
o Type comma
o Type the variable you are taking the derivative
with respect to (…this variable would be x)
o Press enter
for the derivative of f(x) is
Let’s try another derivative. Let gx sinx and hx lnx.
Find g x and h x. You should get the answers shown in
screenshot at the right.
Part II: Finding a Numerical Derivative of a Functions on the TI-89
Let fx sinx.
Suppose we want to find f
3 .
To find a numerical derivative of a function on the TI-89,
o Press 2 nd 8 or F3: CALC: 1: d(differentiate)
o Type the expression (…the right side of the
function).
o Type comma.
o Type the variable you are taking the derivative
with respect to (…this variable would be x).
o Press | key.
o Type x =
o Type the value that you want to evaluate the derivative.
o Press enter.
. Another notation
NOTE: If you evaluate a derivative using the steps above, the calculator will always try to
return an expression. If you would rather the calculator return a numerical value rather than
an expression (an exact answer), you should use nDeriv which is found under F3: Calc. You
will use nDeriv rather then d. The rest of the steps are the same.

Part III: Finding derivatives on the TI-89.
Find the following derivatives using the TI-89. As you find each derivative, try to develop
some rules (…shortcuts) for finding the derivative of a function.
2
3
1) Let fx x . Find f x. 2) Let fx x . Find f x .
5
4 2
3) Let fx x . Find f x. 4) Let fx x x
. Find f x 5) Let fx 7.
Find f x. 6) Let
.
6
1
2 1
. Find f x f x 3x x x
Part IV: Finding numerical derivatives on the TI-89.
Find the following numerical derivatives using the TI-89. Round to three decimal places.
x
7) Let fx x . Find f 2. 8) Let fx 3x x.
Find f 4
. Find f 2
9) Let fx cosx sinx
3
.
5
2
. 10) Let fx x tanx.
Find
at x 2
3
.
11) Write the equation of the tangent line to fx cosx sinx
12) Write the equation of the tangent line to
f x x
.
x
at x 2
f .
.