What is the derivative of f(x)=sec^6(x) ?

The derivative of f(x)=sec^6(x) is 6sec^6(x)tan(x)

What is the first derivative of f(x)=sec^6(x) ?

The first derivative of f(x)=sec^6(x) is 6sec^6(x)tan(x)

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derivative of

f (x) = sec^{6} (x)

6 sec^{6} (x) tan (x)

Solution steps

\frac{d}{d x} (sec^{6} (x))

Apply the chain rule:

6 (sec (x))^{5} \frac{d}{d x} (sec (x))

= 6 (sec (x))^{5} \frac{d}{d x} (sec (x))

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

= 6 (sec (x))^{5} sec (x) tan (x)

Simplify

6 sec^{5} (x) sec (x) tan (x) : 6 sec^{6} (x) tan (x)

= 6 sec^{6} (x) tan (x)

What is the derivative of f(x)=sec^6(x) ?
The derivative of f(x)=sec^6(x) is 6sec^6(x)tan(x)
What is the first derivative of f(x)=sec^6(x) ?
The first derivative of f(x)=sec^6(x) is 6sec^6(x)tan(x)