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#