What is the d/(dt)(sec(t)tan(t)) ?

The d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)

What is the first d/(dt)(sec(t)tan(t)) ?

The first d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

What is the d/(dt)(sec(t)tan(t)) ?
The d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)
What is the first d/(dt)(sec(t)tan(t)) ?
The first d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)