Question

How do you find the derivative of `y=5/(x-3)^2`?

Answer 1

`y'=[-10]/(x-3)^3`

Explanation:

Use Quotient Rule :

`color(red)[y'=(g(x)f'(x)-f(x)g'(x))/(g(x))^2]`

`y=5/(x-3)^2`

`y'=[(x-3)^2*0-5*2(x-3)*1]/(x-3)^4`

`y'=[-10(x-3)]/(x-3)^4`

`y'=[-10]/(x-3)^3`

Answer 2

`dy/dx=-10/(x-3)^3`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`y=5/(x-3)^2=5(x-3)^-2`

`dy/dx=-10(x-3)^-3xxd/dx(x-3)`

`color(white)(dy/dx)=-10/(x-3)^3`