182k views
1 vote
Find the chain rule derivative of sin^(-1)(f(x)).

1 Answer

4 votes

Final answer:

The derivative of sin^(-1)(f(x)) using the chain rule is (f'(x))/(√(1 - (f(x))^2)). This result is obtained by differentiating the outer function with respect to its inner function and then multiplying by the derivative of the inner function.

Step-by-step explanation:

The question asks to find the chain rule derivative of sin-1(f(x)). To apply the chain rule, we start by differentiating the outer function, which is sin-1(u), with respect to its argument u, and then we multiply that by the derivative of the inner function, f(x), with respect to x. In more mathematical terms:

If y = sin-1(u) and u = f(x), then by the chain rule:

  • dy/du = 1/√(1 - u2)
  • du/dx = f'(x)
  • Therefore, dy/dx = dy/du * du/dx = (1/√(1 - u2)) * f'(x) = (1/√(1 - (f(x))2)) * f'(x)

So, the derivative of sin-1(f(x)) with respect to x using the chain rule is (f'(x))/(√(1 - (f(x))2)).

User Rajesh Paul
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories