What is the derivative of-cot(xcsc(x)) ?

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

What is the first derivative of-cot(xcsc(x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

x \to 5 lim (2 x^{2} - 3 x + 7)

f (x) = 1 + cos (x)

\frac{x d x + y d y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} = 0

\frac{d ^{2}}{d x ^{2}} (\frac{8}{9 t ^{4}})

\frac{\partial}{\partial x} (x^{2} + \frac{x}{t} + sin (x))

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