Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = ln (x - 4)^1/2

Answer 1

`(dy)/(dx)=(1)/(2(x-4))`

Explanation:

We are given that a function

`y=ln(x-4)^{(1)/(2)}`

We have to find the derivative of the function

`y=(1)/(2)ln(x-4)`

By using
`lna^b=blna`

Differentiate w.r.t x

`(dy)/(dx)=(1)/(2)* (1)/(x-4)`

By using formula

`(d(lnx))/(dx)=(1)/(x)`

`(dy)/(dx)=(1)/(2(x-4))`

Hence, the derivative of function

`(dy)/(dx)=(1)/(2(x-4))`