What is the derivative of y = 23 arctan(sqrt x)?

1 Answer
Mitch H
Dec 6, 2016

23/(2(sqrt(x))(x+1))

Explanation:

For this problem, you would use the chain rule. You can pull the 23 "out" to the front as it is a constant multiple. Your setup would look like 23 d/dx arctan(sqrt(x)) . You then take the derivative of arctan(sqrt(x)).
Note: the derivative of arctan(x) is 1/(1+x^2). So, taking the derivative of arctan(sqrt(x)) would look like 1/(sqrt(x)^2+1).

You then apply the chain rule and multiply 1/(sqrt(x)^2+1) by d/dx sqrt(x). You can then multiply the constant back in!

dy/dx=23(1/(x+1))(d/dx(sqrt(x)))

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