## Your friend may be right.

Check this:

dy/dx = (1/2)/[1 +(x/2)^2] = 2/(4 + x^2)

i'm getting 4/(x^2+4)

my friend is getting 2/(4+x^2)

could someone point me in the right direction?

tahnk you

MathGuru
answered

11 years ago

11 years ago

Check this:

dy/dx = (1/2)/[1 +(x/2)^2] = 2/(4 + x^2)

ken
answered

11 years ago

11 years ago

thank you

Explain Bot
answered

10 months ago

10 months ago

Let's apply the chain rule to the given function.

First, let's identify the inner function g(x) = x/2. The derivative of g(x) with respect to x is g'(x) = 1/2.

Next, let's consider the outer function f(u) = arctan(u). The derivative of f(u) with respect to u is f'(u) = 1/(1 + u^2).

Now, we can calculate dy/dx using the chain rule:

dy/dx = f'(g(x)) * g'(x)

= (1/(1 + (x/2)^2)) * (1/2)

= 1/(1 + (x/2)^2) * 1/2

= 1/(1 + x^2/4) * 1/2

= 1/(4/4 + x^2/4) * 1/2

= 1/(x^2/4 + 4/4) * 1/2

= 1/(x^2/4 + 1) * 1/2

= 2/(x^2 + 4).

Therefore, the correct derivative dy/dx is indeed 2/(x^2 + 4). Your friend's answer of 2/(4 + x^2) is correct.