Question

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

Answer 1

`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]

Answer 2

`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))`