find the derivative of the function. simplify where possible

Question

find the derivative of the function. simplify where possible 

 

A. y=sin^-1(2x+1)

 

B. y= tan^-1(x-√1+x^2)

 

i got these wrong with the answers in the back of my book. does the -1 mean you flip it or .....

Answer 1

You must recognize that the -1 is NOT an exponent; sin^-1 is a function name; an equivalent is the name arcsin.

The output of this function is an angle (in radians); the input is any number in the interval [-1,1].

 

The derivative of arcsin x is 1/√(1-x²).  In the case A that you mention, don't forget to apply the chain rule; so the derivative is 2/√(1-(2x+1)²).  I will let you simplify.

 

You should know the derivative of arctan x:  1/(1+x²).  Adapt this to the case B & don't forget chain rule