How do you differentiate f(x)=4/sqrt(x-2)f(x)=4x2 using the quotient rule?

1 Answer

f'(x)=(-2)/(x-2)^(3/2)

Explanation:

Quotient rule states that

d/dx[f(x)/(g(x))]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2.

So in this case:

d/dx[4]=0

d/dx[sqrt(x-2)]=1/2(x-2)^(-1/2)*(1)

f'(x)=(sqrt(x-2) * (0)-4(1/2)(x-2)^(-1/2) * (1))/(x-2)

=(-2(x-2)^(-1/2))/(x-2)

=(-2)/(x-2)^(3/2)