How do you use the chain rule to differentiate #g(x)=3tan(4x)#?

1 Answer
Jim G.
Aug 13, 2016

#g'(x)=12sec^2(4x)#

Explanation:

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

#color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(g(h(x)))=g'(h(x))h'(x))color(white)(a/a)|)))......(A)#
#color(blue)"----------------------------------------------------"#

#g(h(x))=3tan(4x)rArrg'(h(x))=3sec^2(4x)#

and #h(x)=4xrArrh'(x)=4#
#color(blue)"-----------------------------------------------------"#
substitute these values into (A)

#rArrg'(x)=3sec^2(4x).4=12sec^2(4x)#

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