What is the derivative of 3*sqrtx - sqrt(x^3)3⋅√x−√x3?

1 Answer
Alan P.
Apr 28, 2015

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)d(3⋅√x−√x3)dx=d(3⋅√x)dx−d(√x3)dx

color(red)((d (3*sqrt(x)))/(dx) = (d (3*x^(1/2)))/(dx))d(3⋅√x)dx=d(3⋅x12)dx

color(red)(=3/2* x^(-1/2))=32⋅x−12

color(blue)((d(sqrt(x^3)))/(dx) = (d (x^(3/2)))/(dx))d(√x3)dx=d(x32)dx

color(blue)=(3/2*x^(1/2))=(32⋅x12)

(d (3*sqrt(x) - sqrt(x^3)))/(dx) = color(red)(3/2*1/sqrt(x))-color(blue)(3/2*sqrt(x))d(3⋅√x−√x3)dx=32⋅1√x−32⋅√x

= 3/2(1/sqrt(x)-sqrt(x))=32(1√x−√x)

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