How do you find the derivative of #f(z)= (z^2+1)/(sqrt z)#?

1 Answer
Jim G.
Mar 5, 2018

#f'(z)=(3z^2-1)/(2sqrt(z^3))#

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)#

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