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Popular >

derivative of 4sec^2(2x)

Solution

\frac{d}{d x} (4 sec^{2} (2 x))

Solution

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

Solution steps

\frac{d}{d x} (4 sec^{2} (2 x))

Take the constant out:

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

= 4 \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

= 4 \cdot 2 sec (2 x) sec (2 x) tan (2 x) \cdot 2

Simplify

4 \cdot 2 sec (2 x) sec (2 x) tan (2 x) \cdot 2 : 16 sec^{2} (2 x) tan (2 x)

= 16 sec^{2} (2 x) tan (2 x)

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derivative of (x^2+3x^2)

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Frequently Asked Questions (FAQ)

What is the derivative of 4sec^2(2x) ?
The derivative of 4sec^2(2x) is 16sec^2(2x)tan(2x)
What is the first derivative of 4sec^2(2x) ?
The first derivative of 4sec^2(2x) is 16sec^2(2x)tan(2x)