How do you find the derivative of the function: #sqrt(19x^2)arccos(3x)#?
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To find the derivative of the function ( \sqrt{19x^2} \cdot \text{arccos}(3x) ), you can use the product rule of differentiation.
The product rule states that if you have two functions ( u(x) ) and ( v(x) ), then the derivative of their product ( u(x)v(x) ) with respect to ( x ) is given by ( u'(x)v(x) + u(x)v'(x) ).
Let ( u(x) = \sqrt{19x^2} ) and ( v(x) = \text{arccos}(3x) ).
Then, find the derivatives ( u'(x) ) and ( v'(x) ), and apply the product rule to get the derivative of the given function.
Here are the steps:

Find ( u'(x) ): [ u'(x) = \frac{d}{dx}(\sqrt{19x^2}) ]

Find ( v'(x) ): [ v'(x) = \frac{d}{dx}(\text{arccos}(3x)) ]

Apply the product rule: [ \frac{d}{dx}(\sqrt{19x^2} \cdot \text{arccos}(3x)) = u'(x)v(x) + u(x)v'(x) ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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