# If y=ln(sin(pi/2)), then what is dy/dx?

Dec 19, 2016

0

#### Explanation:

Geometrical interpretation:

$y = \ln \sin \left(\frac{\pi}{2}\right) = \ln 1 = 0$. So, slope of this line, y'=(0)'=0

This equation represents the x-axis.

The slope of x-axis is 0.

Dec 19, 2016

I tried using your corrected version Miroslav.

#### Explanation:

If you needed $y = \ln \left(\sin \left(\frac{\pi}{x}\right)\right)$
you need to use the Chain Rule: derive first the argument, then the sine and finally the log:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(- \frac{\pi}{x} ^ 2\right) \cdot \cos \left(\frac{\pi}{x}\right) \cdot \frac{1}{\sin} \left(\frac{\pi}{x}\right) = - \frac{\pi}{x} ^ 2 \cdot \cot \left(\frac{\pi}{x}\right)$