# How do you find the derivative of #sqrt(xtanx)#?

Use the chain rule:

So, given:

Now we calculate this derivative using the product rule:

we try to simplify this expression using the trigonometric identity:

Putting it together:

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To find the derivative of sqrt(xtanx), you can use the chain rule. The chain rule states that if you have a composite function u(v(x)), then the derivative is given by u'(v(x)) * v'(x).

Let u(x) = sqrt(x) and v(x) = tan(x).

Then, u'(x) = 1/(2*sqrt(x)) and v'(x) = sec^2(x) (the derivative of tan(x) is sec^2(x)).

Now, applying the chain rule, we have:

(sqrt(xtanx))' = u'(v(x)) * v'(x)

= (1/(2*sqrt(tan(x)))) * sec^2(x)

= sec^2(x) / (2*sqrt(tan(x)))

So, the derivative of sqrt(xtanx) is sec^2(x) / (2*sqrt(tan(x))).

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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.

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.

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.

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