Question #e6c3e

1 Answer
Timber Lin
Dec 14, 2017

#3/2x^(1/2)*ln(3x) + x^(1/2)#

Explanation:

#d/dxf(x) = sqrt(x^3)ln(3x)#
#d/dxf(x) = d/dx(sqrt(x^3))*ln(3x) + d/dxln(3x)*sqrt(x^3)# (product rule)

[side note]
#sqrt(x^3) = x^(3/2)#, so #d/dxsqrt(x^3) = 3/2x^(1/2)# (power rule)
#d/dxln(x) = 1/x# (search up explanation), so #d/dx(ln(3x)) = 1/(3x)*d/dx(3x)# (chain rule) #= 1/(3x)*3 = 1/x#

[back to original problem]
#d/dxf(x) = d/dx(sqrt(x^3))*ln(3x) + d/dxln(3x)*sqrt(x^3) = 3/2x^(1/2)*ln(3x) + 1/x*sqrt(x^3)#
#= 3/2x^(1/2)*ln(3x) + 1/x*x^(3/2)#
#= 3/2x^(1/2)*ln(3x) + x^(1/2)# (exponent rules)

Related questions
Impact of this question
254 views around the world
You can reuse this answer
Creative Commons License