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

The derivative of tan(x-cot(x)) is 4csc^2(2x)

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

The first derivative of tan(x-cot(x)) is 4csc^2(2x)

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

4 csc^{2} (2 x)

Solution steps

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

Simplify

tan (x) - cot (x) : - 2 cot (2 x)

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x) = 2

= - 2 (- csc^{2} (2 x) \cdot 2)

Simplify

= 4 csc^{2} (2 x)

\int \frac{4}{sin ^{2} ( x )} d x

\frac{d}{d x} ((x - 3) x)

x \to + 0 lim (\frac{14}{tan ( x )})

\int 3 x^{2} - 5 x - 7 d x

\frac{d}{d x} (sin (n arcsin (x)))

What is the derivative of tan(x-cot(x)) ?
The derivative of tan(x-cot(x)) is 4csc^2(2x)
What is the first derivative of tan(x-cot(x)) ?
The first derivative of tan(x-cot(x)) is 4csc^2(2x)