Question

Find the value of the derivative for the given function.

Answer 1

1/16

Explanation:

See image for quotient rule

in this case, f(x)=1 and g(x)= √(5-θ)

`(√(5-\theta)*(1')-1*(√(5-\theta))')/((√(5-\theta))^2)\\1'=0\\(√(5-\theta))'=(5-\theta)^(1/2)\\\text{per the chain rule,}\\(√(5-\theta))'=(1/2)*√(5-\theta)^(1/2-1)*-1=(-1)/(2√(5-\theta))\\(√(5-\theta)*(0)-1*((-1)/(2√(5-\theta))\\))/(5-\theta)}\\\\(1)/(2(5-\theta)^(3/2))\\(1)/(2(5-1)^(3/2))= .0625=1/16`