Asked by me
derivative of f(x) = x/(sqrt(x^2-4))
Answers
Answered by
Reiny
I would rewrite it as
y = x(x^2 - 4)^(-1/2_
then use the product rule
dy/dx = x(-1/2)(x^2-4)^(-3/2)(2x) + (x^2-4)^(-1/2)
we could factor that
dy/dx = (x^2-4)^(-3/2)[-x^2 + x^2-4]
= -4/(x^2-4)^(3/2)
check my work, I did not write it on paper first, did all the steps as I typed.
y = x(x^2 - 4)^(-1/2_
then use the product rule
dy/dx = x(-1/2)(x^2-4)^(-3/2)(2x) + (x^2-4)^(-1/2)
we could factor that
dy/dx = (x^2-4)^(-3/2)[-x^2 + x^2-4]
= -4/(x^2-4)^(3/2)
check my work, I did not write it on paper first, did all the steps as I typed.