What is the derivative of 2sec^2(2x) ?

The derivative of 2sec^2(2x) is 8sec^2(2x)tan(2x)

What is the first derivative of 2sec^2(2x) ?

The first derivative of 2sec^2(2x) is 8sec^2(2x)tan(2x)

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\frac{d}{d x} (2 sec^{2} (2 x))

8 sec^{2} (2 x) tan (2 x)

Solution steps

\frac{d}{d x} (2 sec^{2} (2 x))

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 \cdot 2 sec (2 x) sec (2 x) tan (2 x) \cdot 2

Simplify

2 \cdot 2 sec (2 x) sec (2 x) tan (2 x) \cdot 2 : 8 sec^{2} (2 x) tan (2 x)

= 8 sec^{2} (2 x) tan (2 x)

What is the derivative of 2sec^2(2x) ?
The derivative of 2sec^2(2x) is 8sec^2(2x)tan(2x)
What is the first derivative of 2sec^2(2x) ?
The first derivative of 2sec^2(2x) is 8sec^2(2x)tan(2x)