How do you differentiate #f(x) = (4x^3 + 2x) ^ - 4#?

1 Answer
Jim G.
Jun 9, 2016

#(-8(6x^2+1))/(4x^3+2x)^5#

Explanation:

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

f(x) = g(h(x)) then f'(x) = g'(h(x)).h'(x)
#"-------------------------------------------"#

#g(h(x))=(4x^3+2x)^-4rArrg'(h(x))=-4(4x^3+2x)^-5#

#h(x)=4x^3+2xrArrh'(x)=12x^2+2=2(6x^2+1)#
#"-------------------------------------------------------------------------"#
Substitute these values into f'(x)

#f'(x)=-4(4x^3+2x)^-5 .2(6x^2+1)#

#=(-8(6x^2+1))/(4x^3+2x)^5#

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