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

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

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

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

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derivative of

sec^{4} (x)

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

Solution steps

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

Apply the chain rule:

4 (sec (x))^{3} \frac{d}{d x} (sec (x))

= 4 (sec (x))^{3} \frac{d}{d x} (sec (x))

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

= 4 (sec (x))^{3} sec (x) tan (x)

Simplify

4 sec^{3} (x) sec (x) tan (x) : 4 sec^{4} (x) tan (x)

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

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