What is (\partial)/(\partial x)(-2ycsc^3(x)) ?

The answer to (\partial)/(\partial x)(-2ycsc^3(x)) is 6ycsc^3(x)cot(x)

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(\partial)/(\partial x)(-2ycsc^3(x))

\frac{\partial}{\partial x} (- 2 y csc^{3} (x))

6 y csc^{3} (x) cot (x)

Solution steps

\frac{\partial}{\partial x} (- 2 y csc^{3} (x))

Treat

y

as a constant

Take the constant out:

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

= - 2 y \frac{\partial}{\partial x} (csc^{3} (x))

Apply the chain rule:

3 (csc (x))^{2} \frac{\partial}{\partial x} (csc (x))

= 3 (csc (x))^{2} \frac{\partial}{\partial x} (csc (x))

\frac{\partial}{\partial x} (csc (x)) = - cot (x) csc (x)

= - 2 y \cdot 3 (csc (x))^{2} (- cot (x) csc (x))

Simplify

- 2 y \cdot 3 csc^{2} (x) (- cot (x) csc (x)) : 6 y csc^{3} (x) cot (x)

= 6 y csc^{3} (x) cot (x)

What is (\partial)/(\partial x)(-2ycsc^3(x)) ?
The answer to (\partial)/(\partial x)(-2ycsc^3(x)) is 6ycsc^3(x)cot(x)