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How do you find the derivative of #(29arctanx)^(1/2)#?

Answer 1

Samantha Adkison

Let y= #(29arctanx)^(1/2)#

#y^2= 29 arctanx#. Now differentiate w.r.t x

#2ydy/dx= 29/(1+x^2)#

#dy/dx= 29/{2(1+x^2)} 1/(29arctanx)^(1/2)#

=#sqrt29/[2(1+x^2) (arctanx)^(1/2)]#

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Answer 2

Christopher Agresta

To find the derivative of ( (\sqrt{29\arctan(x)}) ), you can use the chain rule. The derivative of ( \sqrt{u} ) with respect to ( x ) is ( \frac{1}{2\sqrt{u}} \cdot \frac{du}{dx} ). Here, ( u = 29\arctan(x) ). Applying the chain rule, the derivative of ( (\sqrt{29\arctan(x)})^{1/2} ) is:

[ \frac{1}{2\sqrt{29\arctan(x)}} \cdot \frac{d(29\arctan(x))}{dx} ]

To find ( \frac{d(29\arctan(x))}{dx} ), you differentiate ( 29\arctan(x) ) with respect to ( x ), which is ( \frac{29}{1+x^2} ). Thus, the derivative is:

[ \frac{1}{2\sqrt{29\arctan(x)}} \cdot \frac{29}{1+x^2} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.