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Popular Calculus >

derivative of tan(x*sec(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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