How do you differentiate #f(x)=(x^2+4x+6)^5#?

1 Answer
Jim G.
Apr 10, 2017

#f'(x)=10(x+2)(x^2+4x+6)^4#

Explanation:

differentiate using the #color(blue)"chain rule"#

#"Given " f(x)=g(h(x))" then"#

#• f'(x)=g'(h(x))xxh'(x)larrcolor(red)" chain rule"#

#rArrf'(x)=5(x^2+4x+6)^4xxd/dx(x^2+4x+6)#

#color(white)(rArrf'(x))=5(x^2+4x+6)^4(2x+4)#

#color(white)(rArrf'(x))=10(x+2)(x^2+4x+6)^4#

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