Derivative of arcsin(x): Understanding the Inverse Trigonometric Derivative Formula

d/dx arcsin(x)

To find the derivative of the function arcsin(x) with respect to x, we can start by using the inverse trigonometric derivative formula

To find the derivative of the function arcsin(x) with respect to x, we can start by using the inverse trigonometric derivative formula.

The derivative of arcsin(x) with respect to x can be written as:

d/dx arcsin(x)

Now, let’s use the inverse trigonometric derivative formula, which states that:

d/dx arcsin(x) = 1 / sqrt(1 – x^2)

So, to calculate the derivative, we need to evaluate 1 / sqrt(1 – x^2).

Note that the domain of arcsin(x) is -1 ≤ x ≤ 1, as the range of arcsin(x) is -π/2 ≤ x ≤ π/2.

Therefore, the derivative of arcsin(x) can be written as:

d/dx arcsin(x) = 1 / sqrt(1 – x^2)

This gives us the derivative of arcsin(x) with respect to x.

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