Differentiate the following functions with respect to x ? y=(x+2) sqrt{x-4}

1 Answer
May 8, 2018

#dy/dx=(3x-6)/(2sqrt(x-4))#

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))#