What is the derivative of 8/(tan^3(x/2)) ?

The derivative of 8/(tan^3(x/2)) is -12cot^2(x/2)csc^2(x/2)

What is the first derivative of 8/(tan^3(x/2)) ?

The first derivative of 8/(tan^3(x/2)) is -12cot^2(x/2)csc^2(x/2)

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derivative of

\frac{8}{tan ^{3} ( \frac{x}{2} )}

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

Solution steps

\frac{d}{d x} (\frac{8}{tan ^{3} ( \frac{x}{2} )})

Simplify

\frac{8}{tan ^{3} ( \frac{x}{2} )} : 8 cot^{3} (\frac{x}{2})

= \frac{d}{d x} (8 cot^{3} (\frac{x}{2}))

Take the constant out:

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

= 8 \frac{d}{d x} (cot^{3} (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (cot (\frac{x}{2})) = - csc^{2} (\frac{x}{2}) \frac{1}{2}

= 8 \cdot 3 (cot (\frac{x}{2}))^{2} (- csc^{2} (\frac{x}{2}) \frac{1}{2})

Simplify

8 \cdot 3 cot^{2} (\frac{x}{2}) (- csc^{2} (\frac{x}{2}) \frac{1}{2}) : - 12 cot^{2} (\frac{x}{2}) csc^{2} (\frac{x}{2})

= - 12 cot^{2} (\frac{x}{2}) csc^{2} (\frac{x}{2})

What is the derivative of 8/(tan^3(x/2)) ?
The derivative of 8/(tan^3(x/2)) is -12cot^2(x/2)csc^2(x/2)
What is the first derivative of 8/(tan^3(x/2)) ?
The first derivative of 8/(tan^3(x/2)) is -12cot^2(x/2)csc^2(x/2)