What is the derivative of-csc(xcot(x)) ?

The derivative of-csc(xcot(x)) is -csc(x)+2csc^3(x)

What is the first derivative of-csc(xcot(x)) ?

The first derivative of-csc(xcot(x)) is -csc(x)+2csc^3(x)

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

- csc (x) + 2 csc^{3} (x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc (x), g = cot (x)

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

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= - ((- cot (x) csc (x)) cot (x) + (- csc^{2} (x)) csc (x))

Simplify

- ((- cot (x) csc (x)) cot (x) + (- csc^{2} (x)) csc (x)) : - csc (x) + 2 csc^{3} (x)

= - csc (x) + 2 csc^{3} (x)

\frac{d y}{d x} + \frac{e}{π} y = 5

\frac{d y}{d x} + y^{3} x + 7 y = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 t^{2} + e^{t} + 1

n = 3 \sum \infty \frac{n !}{2 ^{n + 1}}

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

What is the derivative of-csc(xcot(x)) ?
The derivative of-csc(xcot(x)) is -csc(x)+2csc^3(x)
What is the first derivative of-csc(xcot(x)) ?
The first derivative of-csc(xcot(x)) is -csc(x)+2csc^3(x)