What is the derivative of tan(3xcsc(3x)) ?

The derivative of tan(3xcsc(3x)) is 3sec^2(3x)csc(3x)-3cot(3x)csc(3x)tan(3x)

What is the first derivative of tan(3xcsc(3x)) ?

The first derivative of tan(3xcsc(3x)) is 3sec^2(3x)csc(3x)-3cot(3x)csc(3x)tan(3x)

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\frac{d}{d x} (tan (3 x) csc (3 x))

3 sec^{2} (3 x) csc (3 x) - 3 cot (3 x) csc (3 x) tan (3 x)

Solution steps

\frac{d}{d x} (tan (3 x) csc (3 x))

Apply the Product Rule:

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

f = tan (3 x), g = csc (3 x)

= \frac{d}{d x} (tan (3 x)) csc (3 x) + \frac{d}{d x} (csc (3 x)) tan (3 x)

\frac{d}{d x} (tan (3 x)) = sec^{2} (3 x) \cdot 3

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

= sec^{2} (3 x) \cdot 3 csc (3 x) + (- cot (3 x) csc (3 x) \cdot 3) tan (3 x)

Simplify

= 3 sec^{2} (3 x) csc (3 x) - 3 cot (3 x) csc (3 x) tan (3 x)

What is the derivative of tan(3xcsc(3x)) ?
The derivative of tan(3xcsc(3x)) is 3sec^2(3x)csc(3x)-3cot(3x)csc(3x)tan(3x)
What is the first derivative of tan(3xcsc(3x)) ?
The first derivative of tan(3xcsc(3x)) is 3sec^2(3x)csc(3x)-3cot(3x)csc(3x)tan(3x)