What is the derivative of tan(x/2-cot(x/2)) ?

The derivative of tan(x/2-cot(x/2)) is 1/2 sec^2(x/2)+1/2 csc^2(x/2)

What is the first derivative of tan(x/2-cot(x/2)) ?

The first derivative of tan(x/2-cot(x/2)) is 1/2 sec^2(x/2)+1/2 csc^2(x/2)

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\frac{d}{d x} (tan (\frac{x}{2}) - cot (\frac{x}{2}))

\frac{1}{2} sec^{2} (\frac{x}{2}) + \frac{1}{2} csc^{2} (\frac{x}{2})

Solution steps

\frac{d}{d x} (tan (\frac{x}{2}) - cot (\frac{x}{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (tan (\frac{x}{2})) = sec^{2} (\frac{x}{2}) \frac{1}{2}

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

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

Simplify

= \frac{1}{2} sec^{2} (\frac{x}{2}) + \frac{1}{2} csc^{2} (\frac{x}{2})

\int (2 x - 3) (4 x^{2} + 1) d x

\frac{d}{d x} (\frac{5 x}{x - 2})

x \to - 2 lim (\frac{7}{x ^{2}})

x \to 7 - lim (\frac{( x + 8 )}{x - 7})

\int sin (2 x) \cdot cos (x) d x

What is the derivative of tan(x/2-cot(x/2)) ?
The derivative of tan(x/2-cot(x/2)) is 1/2 sec^2(x/2)+1/2 csc^2(x/2)
What is the first derivative of tan(x/2-cot(x/2)) ?
The first derivative of tan(x/2-cot(x/2)) is 1/2 sec^2(x/2)+1/2 csc^2(x/2)