What is the derivative of #(5x+6)^(1/2)#?

2 Answers
Binayaka C.
Jun 10, 2018

# f^'(x) = 5/(2 sqrt (5 x+6))#

Explanation:

# f(x) = (5 x+6)^(1/2)#

# f^'(x) = 1/2(5 x+6)^(1/2-1)* 5# or

# f^'(x) = 1/2(5 x+6)^(-1/2)* 5# or

# f^'(x) = 5/(2 sqrt (5 x+6))# [Ans]

Jim G.
Jun 10, 2018

#5/(2(5x+6)^(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"#

#d/dx((5x+6)^(1/2))#

#=1/2(5x+6)^(-1/2)xxd/dx(5x+6)#

#=5/(2(5x+6)^(1/2))#

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