How do you find the derivative of the function # (3x-2)/(2x+1)^(1/2)#?

1 Answer
Jul 26, 2017

#(3x+5)/(2x+1)^(3/2)#

Explanation:

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

#"given "f(x)=(g(x))/(h(x))" then"#

#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#

#g(x)=3x-2rArrg'(x)=3#

#"differentiate "(2x+1)^(1/2)" using the "color(blue)"chain rule"#

#h(x)=(2x+1)^(1/2)rArrh'(x)=1/2(2x+1)^(-1/2)xx2#

#color(white)(xxxxxxxxxxxxxxxxxx)=(2x+1)^(-1/2)#

#rArrf'(x)=((2x+1)^(1/2).3-(3x-2)(2x+1)^(-1/2))/((2x+1)^(1/2))^2#

#color(white)(rArrf'(x))=((2x+1)^(-1/2)(3(2x+1)-(3x-2)))/(2x+1)#

#color(white)(rArrf'(x))=(3x+5)/(2x+1)^(3/2)#