Chapter 2: Differentiation
Section 2.3: Differentiation Rules
Example 2.3.3
Apply the rules in Table 2.3.1 to obtain the derivative of fx=5 x2−7 x+12 x3−3x2+x+3.
Solution
Apply the Product rule first. The derivatives needed in the course of applying the Product rule are obtained by applying the Sum, Difference, Constant, Constant Multiple, Identity, and Power rules.
dfdx
=5 x2−7 x+12⋅ddxx3−3x2+x+3+x3−3x2+x+3⋅ddx5 x2−7 x+12
=5 x2−7 x+12⋅3 x2−6 x+1+x3−3x2+x+3⋅10 x−7
=15x4−51x3+83x2−79 x+12+10 x4−37x3+31x2+23x−21
=25x4−88x3+114x2−56 x−9
Maple Solution
Tools≻Load Package: Student Calculus 1
Loading Student:-Calculus1
Control-drag fx=… Context Panel: Assign Function
fx=5 x2−7 x+12 x3−3x2+x+3→assign as functionf
Type f′x and press the Enter key.
Context Panel: Simplify≻Simplify
f′x
10x−7x3−3x2+x+3+5x2−7x+123x2−6x+1
= simplify
25x4−88x3+114x2−56x−9
Note the space between the two sets of parentheses in the definition of fx. This space represents the multiplication operator, and is essential if the explicit multiplication operator is not used.
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