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

1 Answer
Jim G.
Jan 6, 2017

#dy/dx=-45x^2(-5x^3-3)^2#

Explanation:

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

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))#

#"let " u=-5x^3-3rArr(du)/(dx)=-15x^2#

#"and " y=u^3rArr(dy)/(du)=3u^2#

#rArrdy/dx=3u^2(-15x^2)#

change u back into terms of x

#rArrdy/dx=-45x^2(-5x^3-3)^2#

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