What is the derivative of tan(2xcot(2x)) ?

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

What is the first derivative of tan(2xcot(2x)) ?

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

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

2 sec^{2} (2 x) cot (2 x) - 2 csc^{2} (2 x) tan (2 x)

Solution steps

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

Apply the Product Rule:

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

f = tan (2 x), g = cot (2 x)

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

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

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

= sec^{2} (2 x) \cdot 2 cot (2 x) + (- csc^{2} (2 x) \cdot 2) tan (2 x)

Simplify

= 2 sec^{2} (2 x) cot (2 x) - 2 csc^{2} (2 x) tan (2 x)

35

\frac{\partial}{\partial y} (x^{2} y - x y^{2})

y = \frac{tan ( x ) - 1}{sec ( x )}

y^{^{'''}} - 9 y^{^{''}} + y^{^{'}} - 9 y = 0

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