How do you use the chain rule to differentiate #y=(-3x+7)^5#?

1 Answer
Jim G.
Aug 15, 2016

#dy/dx=-15(-3x+7)^4#

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)#
#color(blue)"-------------------------------------------"#

let #u=-3x+7rArr(du)/dx=-3#

and #y=u^5rArr(dy)/(du)=5u^4#
#color(blue)"--------------------------------------------"#
substitute these values into (A) changing u back into terms of x.

#rArrdy/dx=5(-3x+7)^4.(-3)=-15(-3x+7)^4#

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