Differentiate the following functions with respect to x ? y=(x+2) sqrt{x-4}
1 Answer
May 8, 2018
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)larrcolor(blue)"product rule"#
#g(x)=x+2rArrg'(x)=1#
#h(x)=sqrt(x-4)=(x-4)^(1/2)#
#rArrh'(x)=1/2(x-4)^(-1/2)larrcolor(blue)"chain rule"#
#rArrdy/dx=(x+2). 1/2(x-4)^(-1/2)+(x-4)^(1/2)#
#color(white)(rArrdy/dx)=1/2(x-4)^(-1/2)[x+2+2(x-4)]#
#color(white)(rArrdy/dx)=(3x-6)/(2sqrt(x-4))#