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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