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

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Answer 1 · 2015-04-28T01:51:50

By the Derivative Difference Rule
#(d (3*sqrt(x) - sqrt(x^3)))/(dx) = color(red)((d (3*sqrt(x)))/(dx)) - color(blue)((d(sqrt(x^3)))/(dx)#

#color(red)((d (3*sqrt(x)))/(dx) = (d (3*x^(1/2)))/(dx))#

#color(red)(=3/2* x^(-1/2))#

#color(blue)((d(sqrt(x^3)))/(dx) = (d (x^(3/2)))/(dx))#

#color(blue)=(3/2*x^(1/2))#

#(d (3*sqrt(x) - sqrt(x^3)))/(dx) = color(red)(3/2*1/sqrt(x))-color(blue)(3/2*sqrt(x))#

#= 3/2(1/sqrt(x)-sqrt(x))#