What is the derivative of sec(xtan(x)) ?

The derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)

What is the first derivative of sec(xtan(x)) ?

The first derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)

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

- sec (x) + 2 sec^{3} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = tan (x)

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

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

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

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

Simplify

sec (x) tan (x) tan (x) + sec^{2} (x) sec (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

What is the derivative of sec(xtan(x)) ?
The derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)
What is the first derivative of sec(xtan(x)) ?
The first derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)