What is the derivative of #(x-1)(x^2+2)^3#?
1 Answer
Aug 29, 2017
Explanation:
#"differentiate using the "color(blue)"product rule"#
#"given "y=g(x).h(x)" then"#
#dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"#
#g(x)=x-1rArrg'(x)=1#
#h(x)=(x^2+2)^3rArrh'(x)=3(x^2+2)^2.d/dx(x^2+2)#
#color(white)(xxxxxxxxxxxxxxxxxx)=6x(x^2+2)^2#
#rArrdy/dx=6x(x-1)(x^2+2)^2+(x^2+2)^3#
#color(white)(rArrdy/dx)=(x^2+2)^2(6x^2-6x+x^2+2)#
#color(white)(rArrdy/dx)=(x^2+2)^2(7x^2-6x+2)#
