Tuesday, January 23, 2018

Calculus and Its Applications, Chapter 1, Review Exercises, Section Review Exercises, Problem 44

Differentiate g(x)=(5x)2(2x1)5.

By using Product Rule and Chain Rule,

g(x)=(5x)2ddx(2x1)5+(2x1)5ddx(5x)2g(x)=(5x)25(2x1)51ddx(2x1)+(2x1)52(5x)21ddx(5x)g(x)=(5x)25(2x1)4(2)+(2x1)52(5x)(1)g(x)=10(5x)2(2x1)42(5x)(2x1)5g(x)=2(5x)(2x1)4[5(5x)(2x1)]g(x)=2(5x)(2x1)4[255x2x+1]g(x)=2(5x)(2x1)4(267x)g(x)=2(5x)(267x)(2x1)4

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