How do you find the derivative of $sqrt(x+1)$ ?

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Answer 1 · 2015-05-14T16:02:09

Using the chain rule!

Let's name your function $y$ , as $y = sqrt(x+1)$

Let's consider $u = x+1$ and now derive $y = sqrt(u)$ (which is the same as $y=u^(1/2)$

$(dy)/(du) = (1/2)*u^(-1/2) = 1/(2u^(1/2))$

However, we have already stated that $u = x+1$ . So,
$(du)/(dx) = 1$

and

$(dy)/(du) * (du)/(dx) = dy/dx " (chain rule)"$

So

$(dy)/(dx) = 1/(2*(x+1)^(1/2))*(1) = 1/(2sqrt(x+1))$

How do you find the derivative of sqrt(x+1)sqrt(x+1)?