Answer:
[tex]\frac{dy}{dx} = -\frac{b}{x^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{b}{x}[/tex]
Required
Determine the first derivative
Rewrite the expression as:
[tex]y =\frac{b}{x}[/tex]
Apply law of indices
[tex]y =bx^{-1}[/tex]
An equation with the form
[tex]y = ax^n[/tex]
has the derivative:
[tex]\frac{dy}{dx} = nax^{n-1}[/tex]
So, the derivative of [tex]y =bx^{-1}[/tex] is
[tex]\frac{dy}{dx} = -1 * bx^{-1-1}[/tex]
[tex]\frac{dy}{dx} = -bx^{-2}[/tex]
[tex]\frac{dy}{dx} = -\frac{b}{x^2}[/tex]
