1 answer

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

Question:

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

Answers

#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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