What is the derivative of #3*(sqrt x) - (sqrtx^3)#?

1 Answer
Mar 11, 2016

Answer:

#d/(d x)(3*sqrt x-sqrt (x^3))=3/2*((sqrtx-sqrt2))/x#

Explanation:

#d/(d x)(3*sqrt x-sqrt (x^3))=?#
#(3*1)/(2sqrt x)-(3x^2)/(2sqrt(x^3))#
#(3*1)/(2sqrt x color(green)(sqrt (x^3)))-(3x^2)/(2sqrt(x^3)color(green)(sqrt2))#
#(3sqrt (x^3)-3x^2sqrt2)/(2sqrt(x^4))#
#(3sqrt (x^3)-3x^2sqrt2)/(2x^2)#
#(3cancel(x))/(2)((sqrtx-xsqrt2)/cancel((x^2)))#
#d/(d x)(3*sqrt x-sqrt (x^3))=3/2*((sqrtx-sqrt2))/x#