Final answer:
To find the derivative of y=arccot(x²), use the chain rule to multiply the derivative of arccot(u) with u=x² by the derivative of x², resulting in dy/dx = -2x / (1+x´).
Step-by-step explanation:
If y=arccot(x²), to find dy/dx, we use chain rule for differentiation. We first find the derivative of the outer function, arccot(u), with respect to u and then multiply it by the derivative of the inner function, u=x², with respect to x.
The derivative of arccot(u) with respect to u is -1/(1+u²). The derivative of u=x² with respect to x is 2x. Now applying the chain rule gives us:
dy/dx = (d(arccot(u))/du) · (du/dx)
dy/dx = -1/(1+(x²)²) · 2x
So, dy/dx = -2x / (1+x´).