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How do you find the derivative of the function #g(x) = sqrt(1 - 121 x^2)(arccos)(11 x)#?

Answer 1

Cameron Alexander

In this way:

#y'=1/(2sqrt(1-121x^2))*(-242x)*arccos(11x)+#

#+sqrt(1-121x^2) * (-1/sqrt(1-121x^2) *11)=#

#=-(121x)/sqrt(1-121x^2)arccos(11x)-11#.

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Answer 2

Ezra Adams

To find the derivative of the function ( g(x) = \sqrt{1 - 121x^2} \cdot \text{arccos}(11x) ), you can use the product rule of differentiation.

First, differentiate each term separately:

Differentiate ( \sqrt{1 - 121x^2} ) with respect to ( x ).
Differentiate ( \text{arccos}(11x) ) with respect to ( x ).

Then, apply the product rule, which states that if ( u(x) ) and ( v(x) ) are differentiable functions, then the derivative of their product ( u(x) \cdot v(x) ) is given by ( u'(x) \cdot v(x) + u(x) \cdot v'(x) ).

After finding the derivatives of each term and applying the product rule, you can combine the results to obtain the derivative of ( g(x) ).

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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.