What is the derivative of 1/(sin(x-y)) ?

The derivative of 1/(sin(x-y)) is -cot(x-y)csc(x-y)

What is the first derivative of 1/(sin(x-y)) ?

The first derivative of 1/(sin(x-y)) is -cot(x-y)csc(x-y)

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derivative of

\frac{1}{sin ( x - y )}

- cot (x - y) csc (x - y)

Solution steps

\frac{d}{d x} (\frac{1}{sin ( x - y )})

Simplify

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

= \frac{d}{d x} (csc (x - y))

Treat

y

as a constant

Apply the chain rule:

- cot (x - y) csc (x - y) \frac{d}{d x} (x - y)

= - cot (x - y) csc (x - y) \frac{d}{d x} (x - y)

\frac{d}{d x} (x - y) = 1

= - cot (x - y) csc (x - y) \cdot 1

Simplify

= - cot (x - y) csc (x - y)

(x + 1) (x - 2)^{2}

f (x) = cos^{4} (x) - 2 x^{2}

(4 u)^{3}

\frac{d}{d q} (\frac{k \cdot q ^{1} \cdot q ^{2}}{r ^{2}})

f (x) = (5 x + 4)^{2}

What is the derivative of 1/(sin(x-y)) ?
The derivative of 1/(sin(x-y)) is -cot(x-y)csc(x-y)
What is the first derivative of 1/(sin(x-y)) ?
The first derivative of 1/(sin(x-y)) is -cot(x-y)csc(x-y)