Question

First derivative of b/x ​

Answer 1

Answer:

$\frac{dy}{dx} = -\frac{b}{x^2}$

Step-by-step explanation:

Given

$\frac{b}{x}$

Required

Determine the first derivative

Rewrite the expression as:

$y =\frac{b}{x}$

Apply law of indices

$y =bx^{-1}$

An equation with the form

$y = ax^n$

has the derivative:

$\frac{dy}{dx} = nax^{n-1}$

So, the derivative of $y =bx^{-1}$ is

$\frac{dy}{dx} = -1 * bx^{-1-1}$

$\frac{dy}{dx} = -bx^{-2}$

$\frac{dy}{dx} = -\frac{b}{x^2}$