What is the derivative of xcot(5/(x^2)) ?

The derivative of xcot(5/(x^2)) is cot(5/(x^2))+(10csc^2(5/(x^2)))/(x^2)

What is the first derivative of xcot(5/(x^2)) ?

The first derivative of xcot(5/(x^2)) is cot(5/(x^2))+(10csc^2(5/(x^2)))/(x^2)

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\frac{d}{d x} (x cot (\frac{5}{x ^{2}}))

cot (\frac{5}{x ^{2}}) + \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{2}}

Solution steps

\frac{d}{d x} (x cot (\frac{5}{x ^{2}}))

Apply the Product Rule:

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

f = x, g = cot (\frac{5}{x ^{2}})

= \frac{d x}{d x} cot (\frac{5}{x ^{2}}) + \frac{d}{d x} (cot (\frac{5}{x ^{2}})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cot (\frac{5}{x ^{2}})) = \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{3}}

= 1 \cdot cot (\frac{5}{x ^{2}}) + \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{3}} x

Simplify

1 \cdot cot (\frac{5}{x ^{2}}) + \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{3}} x : cot (\frac{5}{x ^{2}}) + \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{2}}

= cot (\frac{5}{x ^{2}}) + \frac{10 csc ^{2} ( \frac{5}{x ^{2}} )}{x ^{2}}

\frac{x ^{2}}{x - 6}

\frac{d}{d x} (\frac{2 cos ( 2 x ) - 1}{2 cos ( x )})

\frac{\partial}{\partial y} (1 + e^{x} y + x e^{x} y)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 4} e^{3 t}

f (x) = (2 x - 8)^{5}

What is the derivative of xcot(5/(x^2)) ?
The derivative of xcot(5/(x^2)) is cot(5/(x^2))+(10csc^2(5/(x^2)))/(x^2)
What is the first derivative of xcot(5/(x^2)) ?
The first derivative of xcot(5/(x^2)) is cot(5/(x^2))+(10csc^2(5/(x^2)))/(x^2)