What is the derivative of 4sec^2(4x) ?

The derivative of 4sec^2(4x) is 32sec^2(4x)tan(4x)

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

The first derivative of 4sec^2(4x) is 32sec^2(4x)tan(4x)

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

32 sec^{2} (4 x) tan (4 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (4 x)) = sec (4 x) tan (4 x) \cdot 4

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

Simplify

4 \cdot 2 sec (4 x) sec (4 x) tan (4 x) \cdot 4 : 32 sec^{2} (4 x) tan (4 x)

= 32 sec^{2} (4 x) tan (4 x)

What is the derivative of 4sec^2(4x) ?
The derivative of 4sec^2(4x) is 32sec^2(4x)tan(4x)
What is the first derivative of 4sec^2(4x) ?
The first derivative of 4sec^2(4x) is 32sec^2(4x)tan(4x)