Chapter 2: Differentiation
Section 2.3: Differentiation Rules
Apply the rules in Table 2.3.1 to obtain the derivative of fx=5 x2−7 x+12 x3−3⁢x2+x+3.
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.
=5 x2−7 x+12⋅ddxx3−3⁢x2+x+3+x3−3⁢x2+x+3⋅ddx5 x2−7 x+12
=5 x2−7 x+12⋅3 x2−6 x+1+x3−3⁢x2+x+3⋅10 x−7
=15⁢x4−51⁢x3+83⁢x2−79 x+12+10 x4−37⁢x3+31⁢x2+23⁢x−21
Tools≻Load Package: Student Calculus 1
Context Panel: Assign Function
fx=5 x2−7 x+12 x3−3⁢x2+x+3→assign as functionf
Type f′x and press the Enter key.
Context Panel: Simplify≻Simplify
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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