How do you find the derivative of #f(z)= (z^2+1)/(sqrt z)#?
1 Answer
Mar 5, 2018
Explanation:
#"differentiate using the "color(blue)"quotient rule"#
#"given "f(z)=(g(z))/(h(z))" then"#
#f'(z)=(h(z)g'(z)-g(z)h'(z))/(h(z))^2larrcolor(blue)"quotient rule"#
#g(z)=z^2+1rArrg'(z)=2z#
#h(z)=z^(1/2)rArrh'(z)=1/2z^(-1/2)#
#rArrf'(z)=(2z^(3/2)-1/2z^(-1/2)(z^2+1))/z#
#color(white)(rArrf'(z))=(1/2z^(-1/2)(4z^2-z^2-1))/z#
#color(white)(rArrf'(z))=(3z^2-1)/(2z^(3/2))=(3z^2-1)/(2sqrt(z^3)#
