Question

What is the result of d(Arctan(x)/dx)?

A) ¹∕₍₁₊ₓ²₎
B) ¹/ₐ₍₁₊(ˣ∕ₐ)²₎
C) ᵃ∕₍ₐ²₊ₓ²₎
D) Arctan(x) + C

Answer 1

The result of
`d(Arctan(x)/dx) is 1/(1+x^2).`

Step-by-step explanation:

The derivative of
`Arctan(x)` with respect to x, denoted as
`d(Arctan(x))/dx`, can be found using the chain rule.

`Let y = Arctan(x).`

The chain rule states that
`d(Arctan(x))/dx = dy/dx = dy/dt * dt/dx.`In this case,
`dt/dx = 1,` since
`t = x.` The derivative of
`Arctan(t)` with respect to
`t, dy/dt,` can be found using the derivative of inverse trigonometric functions.

The derivative o
`f Arctan(t) is 1/(1+t^2).`

Therefore,
`d(Arctan(x))/dx = 1/(1+x^2).`