# How do I find the derivative of the function #y=ln (sqrt(x^2-9))#?

##### 1 Answer

Jan 27, 2015

The derivative of this function is:

It is important to remember which is the derivative of the

- The derivative of
#y=ln[f(x)]# is#y'=(f'(x))/f(x)# . - The derivative of
#y=sqrt(f(x))# is#y'=(f'(x))/(2sqrt(f(x)))# . - The derivative of
#y=[f(x)]^n# is#y'=n[f(x)]^(n-1)f'(x)# . - The theorem of the function of function derivation says that the derivative of
#y=[f(g(x))]# is#y'=f'(g(x))g'(x)# .

There is another way to do this derivative, rememberig one property of the logarithmic function:

so:

and the derivative of this function is easier: