# Double check a Calculus problem

1. Sep 15, 2015

### loulou86

1. The problem statement, all variables and given/known data
Differentiate with respect to the variable
y=cos^-1((x/4)

2. Relevant equations
cos^-1 x/a
inverse cosine function
-1/root a^2-x^2
3. The attempt at a solution
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?

2. Sep 15, 2015

### RUber

What you have written is difficult to read. Please use latex, and if nothing else, use parentheses.
$\cos^{-1} \frac{x}{a} = -\frac{1}{\sqrt{a^2 - x^2}}.$
In the problem you are given, a = 4.
You should be able to take the derivative using the chain rule for $- (a^2 - x^2)^{-1/2}$.
I have no clue where your 3 or .3 came from.

3. Sep 15, 2015

### Staff: Mentor

Problems with derivatives belong in the Calculus section, not in the Precalc section.
The above is the formula for the derivative of the inverse cosine.

Also, you need parentheses to indicate what's in the radical -- -1/root (a^2-x^2)
Where did the 3 come from? And what happened to the minus sign?

Last edited: Sep 15, 2015
4. Sep 15, 2015

### loulou86

I've unintentionally left out part of the question. Reworked...

1. The problem statement, all variables and given/known data
Differentiate with respect to the variable
y= (1/3) cos^-1 ((x/4)

2. Relevant equations
cos^-1 (x/a)
inverse cosine function
-1/root(a^2-x^2)
3. The attempt at a solution
Differentiated
dy/dx=(1/root(4^2-x^2))/3

Could you comment on whether now this clears up you queries.

Thanks

5. Sep 15, 2015

### Staff: Mentor

Better: d/dx(cos-1(x/a)) = -1/√(a2 - x^2)
Where did your minus sign go?

6. Sep 15, 2015

### loulou86

I was under the impression that the -1 goes because of the (1/3)

7. Sep 15, 2015

### Staff: Mentor

No. I don't know why you would think that.

8. Sep 15, 2015

### loulou86

I assume i am totally wrong in that case

9. Sep 15, 2015

### Staff: Mentor

d/dx[(1/3) cos-1 ((x/4)] = (1/3) * d/dx[cos-1 ((x/4)] (derivative of a constant multiple rule for differentiation)
= (1/3) * ?