What is (\partial)/(\partial x)((sin(x))/(sin(y))) ?

The answer to (\partial)/(\partial x)((sin(x))/(sin(y))) is cos(x)csc(y)

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(\partial)/(\partial x)((sin(x))/(sin(y)))

\frac{\partial}{\partial x} (\frac{sin ( x )}{sin ( y )})

cos (x) csc (y)

Solution steps

\frac{\partial}{\partial x} (\frac{sin ( x )}{sin ( y )})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{sin ( y )} \frac{\partial}{\partial x} (sin (x))

Apply the common derivative:

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= \frac{1}{sin ( y )} cos (x)

Simplify

\frac{1}{sin ( y )} cos (x) : cos (x) csc (y)

= cos (x) csc (y)

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What is (\partial)/(\partial x)((sin(x))/(sin(y))) ?
The answer to (\partial)/(\partial x)((sin(x))/(sin(y))) is cos(x)csc(y)