Question

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

Answer 1

Answer:

$\frac{dy}{dx}=\frac{1}{2(x-4)}$

Step-by-step explanation:

We are given that a function  

$y=ln(x-4)^{\frac{1}{2}}$

We have to find the derivative of the function

$y=\frac{1}{2}ln(x-4)$

By using $lna^b=blna$

Differentiate w.r.t x

$\frac{dy}{dx}=\frac{1}{2}\times \frac{1}{x-4}$

By using formula

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=\frac{1}{2(x-4)}$

Hence, the derivative of function

$\frac{dy}{dx}=\frac{1}{2(x-4)}$