How do you find the derivative of #sqrt(2x+3)#?

1 Answer
Topscooter
Jan 3, 2016

The derivative of this function is #1/(sqrt(2x+3))#.

Explanation:

Let #h(x) = sqrt(2x+3)#. You see that that #h = f @ g# with #f(x) = sqrtx# and #g(x) = 2x+3#.

By the chain rule, #h'(x) = g'(x)*(f'@g)(x) = g'(x)*f'(g(x))#.

Here, #f'(x) = 1/(2sqrtx)# and #g'(x) = 2#.

So #h'(x) = 2*1/(2sqrt(2x+3)) = 1/(sqrt(2x+3))#

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