Problem

(b) Let A(x)=(x−2)2(3x−4)2 Find A′(x) in fully factorised form

Answer

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Answer

A′(x)=(x−2)2(18x−24)+2(x−2)(3x−4)2

Steps

Step 1 ：Let A(x)=(x−2)2(3x−4)2

Step 2 ：Find the derivatives of (x−2)2 and (3x−4)2 using the chain rule:

Step 3 ：ddx(x−2)2=2(x−2)

Step 4 ：ddx(3x−4)2=2(3x−4)(3)

Step 5 ：Apply the product rule to find A′(x):

Step 6 ：A′(x)=(x−2)2(2(3x−4)(3))+(2(x−2))(3x−4)2

Step 7 ：Simplify the expression:

Step 8 ：A′(x)=(x−2)2(6(3x−4))+2(x−2)(3x−4)2

Step 9 ：A′(x)=(x−2)2(18x−24)+2(x−2)(3x−4)2

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