How do you use the chain rule to differentiate #sin(e^(6x))#?

1 Answer
Jim G.
Jul 29, 2016

#6e^(6x) cos(e^(6x))#

Explanation:

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

#color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=dy/(du)xx(du)/(dx))color(white)(a/a)|)))........(A)#

#rArry=sin(e^(6x))#

let #color(blue)(u=e^(6x))rArr(du)/dx=e^(6x).d/dx(6x)=6e^(6x)#

and #y=sincolor(blue)(u)rArr(dy)/(du)=coscolor(blue)(u)#

substitute these values into (A) converting u into terms of x

#rArrdy/dx=cosu.6e^(6x)=6e^(6x)cos(e^(6x))#

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