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

2 Answers
Jun 3, 2018

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

Jun 3, 2018

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