What is the derivative of #(x-1)(x^2+2)^3#?

1 Answer
May 20, 2018

Answer:

#(x^2+2)^2(7x^2-6x+2)#

Explanation:

#"differentiate using the "color(blue)"product/chain rules"#

#"given "y=g(x)h(x)" then"#

#dy/dx=g(x)h'(x)+h(x)g'(x)larrcolor(blue)"product rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#g(x)=x-1rArrg'(x)=1#

#h(x)=(x^2+2)^3rArrh'(x)=3(x^2+2)^2xx2x#

#color(white)(xxxxxxxxxxxxxxxxxx)=6x(x^2+2)^2#

#rArrd/dx((x-1)(x^2+2)^3)#

#=6x(x-1)(x^2+2)^2+(x^2+2)^3#

#=(x^2+2)^2[6x(x-1)+x^2+2]#

#=(x^2+2)^2(7x^2-6x+2)#