What is the derivative of 3cot(2xsec(2x)) ?

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

What is the first derivative of 3cot(2xsec(2x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d ^{2}}{d x ^{2}} (x^{4} - 2 x^{3})

\frac{d}{d x} (\frac{2 x + x ^{2}}{( 1 + x ) ^{2}})

\frac{d}{d x} (e^{x^{2} + x + 1})

\frac{6}{( 1 - x ) ^{3}}

\frac{d}{d t} (\frac{t ^{4}}{4})

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