Question

Plz help derive ln(sinx)​

Answer 1

Answer:

Step-by-step explanation:

I'm assuming you want to find the derivative of the function y = ln (sin x).

If this is the case, let's look at the derivatives of y = ln x and y = sin x separately and then use the results as appropriate:

(d/dx) ln x = 1/x

(d/dx) ln u = (1/u)(du/dx)

(d/dx) sin x = cos x

We'll also need to use the Chain Rule (which we have done in finding the derivative of ln u, above).

                                  1                                       1                        cos x

(d/dx) ln (sin x) = ------------- * (d/dx) (sin x) = ----------- * cos x = ------------ = cot x

                               sin x                                 sin x                      sin x

Answer 2

Answer:

cot(x)

Step-by-step explanation:

$\frac{d}{dx}$ln(sin(x)) = $\frac{1}{sin(x)} *cos(x)$ = $\frac{cos(x)}{sin(x)} = cot(x)$