]Find the derivative of f(x) = x 2+2 cos2 (4x)?

1 Answer
Jim G.
May 4, 2018

#f'(x)=2x-8sin8x#

Explanation:

#"differentiate "2cos^2(4x)" using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#rArr2cos^2(4x)=2(cos4x)^2#

#d/dx(2(cos4x)^2)#

#=4cos4x xxd/dx(cos4x)#

#=4cos4x xx-sin4x xxd/dx(4x)#

#=-16sin4xcos4x=-8sin8x#

#rArrf'(x)=2x-8sin8x#

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