Question

Find dy/dx of y = cos⁻¹ (1 -x²/ 1 + x²), 0

Answer 1

To find dy/dx of y = cos⁻¹ (1 -x²/ 1 + x²), we can use the chain rule. Let's start by simplifying the expression inside the inverse cosine function: (1 - x²/ 1 + x²). Simplifying this gives us (1 - x²)/(1 + x²). Now, we can differentiate y = cos⁻¹((1 - x²)/(1 + x²)) with respect to x.

Step-by-step explanation:

To find dy/dx of y = cos⁻¹ (1 -x²/ 1 + x²), we can use the chain rule. Let's start by simplifying the expression inside the inverse cosine function: (1 - x²/ 1 + x²). Simplifying this gives us (1 - x²)/(1 + x²). Now, we can differentiate y = cos⁻¹((1 - x²)/(1 + x²)) with respect to x.

Using the chain rule, we have:

• dy/dx = -1/sqrt(1 - ((1 - x²)/(1 + x²))²) * d((1 - x²)/(1 + x²))/dx
• dy/dx = -1/sqrt(1 - ((1 - x²)/(1 + x²))²) * ((-2x(1 + x²) - 2(1 - x²))/((1 + x²)²))

Now, we can simplify the expression further if needed.