How do you differentiate #y=(1-x^2)^10#?

1 Answer
Jim G.
Feb 22, 2017

#dy/dx=-20x(1-x^2)^9#

Explanation:

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

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

#"let "u=1-x^2rArr(du)/(dx)=-2x#

#"then "y=u^10rArr(dy)/(du)=10u^9#

#rArrdy/dx=10u^9.(-2x)#

convert u back into terms of x and simplify.

#rArrdy/dx=-20x(1-x^2)^9#

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