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What is the derivative of this function #y=cos^-1(2x+1)#?

Answer 1

Charles Anctil

#(dy)/(dx)=-2/sqrt(1-(2x+1)^2)#

As #y=cos^(-1)(2x+1)#, we have

#cosy=2x+1# and differentiating it using chain rule, we get

#-siny xx (dy)/(dx)=2# or

#(dy)/(dx)=-2/siny=-2/sqrt(1-cos^2y)=-2/sqrt(1-(2x+1)^2)#

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Answer 2

Ezekiel Alexander

The derivative of the function ( y = \cos^{-1}(2x + 1) ) is given by:

[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 - (2x + 1)^2}} \times 2 ]

[ = -\frac{2}{\sqrt{1 - (2x + 1)^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.