Double check a Calculus problem

[loulou86]

Homework Statement

Differentiate with respect to the variable
y=cos^-1((x/4)

Homework Equations

cos^-1 x/a
inverse cosine function
-1/root a^2-x^2

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 can't really see how to simplify this further.

Can it be done. are the current steps correct?

 

[RUber]

What you have written is difficult to read. Please use latex, and if nothing else, use parentheses.
You start with:
$\cos^{-1} \frac{x}{a} = -\frac{1}{\sqrt{a^2 - x^2}}.$
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.

 

[Mark44]

Problems with derivatives belong in the Calculus section, not in the Precalc section.

Homework Statement

Differentiate with respect to the variable
y=cos^-1((x/4)

Homework Equations

cos^-1 x/a
inverse cosine function
-1/root a^2-x^2

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)

The Attempt at a Solution

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

Where did the 3 come from? And what happened to the minus sign?

Brought in the 3 for
dy/dx=0.3x(1/root4^2-x^2)

at this point i can't really see how to simplify this further.

Can it be done. are the current steps correct?

 

[loulou86]

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

Homework Statement

Differentiate with respect to the variable
y= (1/3) cos^-1 ((x/4)

Homework Equations

cos^-1 (x/a)
inverse cosine function
-1/root(a^2-x^2)

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

 

[Mark44]

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

Homework Statement

Differentiate with respect to the variable
y= (1/3) cos^-1 ((x/4)

Homework Equations

cos^-1 (x/a)
inverse cosine function
-1/root(a^2-x^2)

Better: d/dx(cos^-1(x/a)) = -1/√(a² - x^2)

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.

Where did your minus sign go?

 

[loulou86]

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

 

[Mark44]

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

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

 

[loulou86]

I assume i am totally wrong in that case

 

[Mark44]

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) * ?