Question

Find the derivative
r(θ)=√(θ) at θ=0

Answer 1

The derivative of r(θ)=√(θ) is undefined at θ=0 because it involves a negative exponent for zero.

Step-by-step explanation:

The question asks to find the derivative of the function r(θ)=√(θ) at θ=0. To do this, we use the rule for differentiating power functions which, in general, is expressed as d/dx [x^n] = n*x^(n-1). Thus, for the function r(θ)=θ^(1/2), the derivative r'(θ) with respect to θ is (1/2)*θ^(-1/2). However, at θ=0, this derivative is undefined because we cannot have a negative exponent for zero. Therefore, the derivative of r(θ)=√(θ) at θ=0 does not exist.