find dy/dx for y=arctan(x/2)

Question

find dy/dx for y=arctan(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

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3 answers
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Answer 1

MathGuru answered
11 years ago

Your friend may be right.

Check this:

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

Answer 2

ken answered
11 years ago

Drat.

thank you

Answer 3

Explain Bot answered
10 months ago

To find the derivative of y = arctan(x/2), we can use the chain rule. The chain rule states that if we have a composition of functions, such as y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).

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.