Chapter 2: Differentiation
Section 2.4: The Chain Rule
Use the Chain rule to obtain the derivative of Fx=x−πx2−47.
Context Panel: Assign Function
Fx=x−πx2−47→assign as functionF
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
F′x = 7⁢x−π6x2−47−14⁢x−π7⁢xx2−48= simplify 7⁢−x+π6⁢−x2−4+2⁢x⁢πx2−48
Define f⁡u⁢=⁢u7 as the "outer" function, and g⁡x⁢=⁢x⁢−⁢πx2⁢−⁢4 as the "inner" function, so that f⁡x⁢=⁢f⁡g⁡x. The Chain rule applies first, but the derivative of g, the "inner" function, requires the Quotient rule.
=7 g6x ddx⁢x⁢−⁢πx2⁢−⁢4
=7 x−πx2−46 −x2+2⁢π⁢x−4x2−42
=7π−x62 π x−x2−4x2−48
This calculation can be implemented interactively in the
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