What is (\partial)/(\partial x)(1/(tan(xy))) ?

The answer to (\partial)/(\partial x)(1/(tan(xy))) is -csc^2(xy)y

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(\partial)/(\partial x)(1/(tan(xy)))

\frac{\partial}{\partial x} (\frac{1}{tan ( x y )})

- csc^{2} (x y) y

Solution steps

\frac{\partial}{\partial x} (\frac{1}{tan ( x y )})

Simplify

\frac{1}{tan ( x y )} : cot (x y)

= \frac{\partial}{\partial x} (cot (x y))

Treat

y

as a constant

Apply the chain rule:

- csc^{2} (x y) \frac{\partial}{\partial x} (x y)

= - csc^{2} (x y) \frac{\partial}{\partial x} (x y)

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

= - csc^{2} (x y) y

\frac{d y}{d x} = (x + y + 2)^{2}

\frac{\partial}{\partial x} (e^{- 2 x} \cdot cos (2 y))

\int \frac{5 x - 3}{x ^{2} - 1} d x

y = \frac{6}{x}

\int 7 (sin (x))^{4} (cos (x))^{2} d x

What is (\partial)/(\partial x)(1/(tan(xy))) ?
The answer to (\partial)/(\partial x)(1/(tan(xy))) is -csc^2(xy)y