What is the derivative of #(3+2x)^(1/2)#?

2 Answers
Jim G.
May 2, 2018

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

Explanation:

#"differentiate using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#rArrd/dx((3+2x)^(1/2))#

#=1/2(3+2x)^(-1/2)xxd/dx(3+2x)#

#=1(3+2x)^(-1/2)=1/((3+2x)^(1/2))#

Oliver S.
May 2, 2018

#1/(sqrt(3+2x))#

Explanation:

If
#f(x)=(3+2x)^(1/2)=(sqrt(3+2x))#

(apply the chain rule)

#u=3+2x#

#u'=2#

#f(u)=u^(1/2)#

#f'(u)=(1/2) (u)^(-1/2) times u'#

Hence:

#f'(x)=(1/2) (3+2x)^(-1/2) times 2#

#f'(x)=(3+2x)^(-1/2)#

#f'(x)=(1)/(sqrt(3+2x))#

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