Hi all i have a calculus problem

 

Differentiate with respect to the variable

 

y=1/3cos-1(x/4)

 

i completed this using the inverse cosine function

y=cos-1(x^-4)/3 function -1/root a^2-x^2

 

Differentiated

dy/dx=(1/root4^2-x^2)/3

 

Brought in the 3 for

dy/dx=0.3x(1/root4^2-x^2)

 

at this point i cant really see how to simplify this further.

 

Can it be done. are the current steps correct?

 

Thank you

 

 

Your answer seems ok but missing a negative - but your simplification and bracketing is woeful

 

1/3 DOES NOT EQUAL 0.3

 

I get

 

\frac{dy}{dx}=-\frac{1}{3 \sqrt{16-x^2}}

 

[latex]\frac{dy}{dx}=-\frac{1}{3 \sqrt{16-x^2}}[/latex]