Problem 48 - Calculus of a Single Variable

Question

Find the derivative of the function. \(f(x)=\arcsin x+\arccos x\)

Step-by-Step Solution

Answer

The derivative of the function \(f(x)=\arcsin x+\arccos x\) is 0.

Step 1: Derivative of Arcsin(x)

First, derive the function 'arcsin x'. The derivative of 'arcsin x' is \( \frac{1}{\sqrt{1-x^2}} \).

Step 2: Derivative of Arccos(x)

Next, derive the function 'arccos x'. The derivative of 'arccos x' is \( -\frac{1}{\sqrt{1-x^2}} \).

Step 3: Sum results

Finally, add the results obtained in the previous steps. Therefore, \( \frac{1}{\sqrt{1-x^2}} - \frac{1}{\sqrt{1-x^2}} = 0 \).