Finding the Derivative of f(sin⁻¹ x) Using the Chain Rule in Mathematics

f'(sin⁻¹x)

To find the derivative of the function f(sin⁻¹ x), we can use the chain rule

To find the derivative of the function f(sin⁻¹ x), we can use the chain rule.

Let’s start by defining a new function g(x) = sin⁻¹ x.

The derivative of g(x) with respect to x, denoted as g'(x), can be found by using the formula for the derivative of the inverse function.

g'(x) = 1/√(1 – x²).

Now, we can apply the chain rule to find the derivative of f(sin⁻¹ x).

f'(sin⁻¹ x) = f'(g(x)).

Using the chain rule, we know that the derivative of f(g(x)) with respect to x is given by:

f'(g(x)) * g'(x).

Substituting the values we have:

f'(sin⁻¹ x) = f'(g(x)) * g'(x).

Therefore, the derivative of f(sin⁻¹ x) is given by f'(g(x)) multiplied by g'(x), which is:

f'(sin⁻¹ x) = f'(g(x)) * g'(x) = f'(sin⁻¹ x) * 1/√(1 – x²).

Note: This is a general form of the derivative of f(sin⁻¹ x). If you provide a specific function f(x), then it can be further simplified by finding the derivative of f(x) and substituting it into the equation.

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