What is the derivative of sec(θ)tan(θ) ?

The derivative of sec(θ)tan(θ) is -sec(θ)+2sec^3(θ)

What is the first derivative of sec(θ)tan(θ) ?

The first derivative of sec(θ)tan(θ) is -sec(θ)+2sec^3(θ)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

sec (θ) tan (θ)

- sec (θ) + 2 sec^{3} (θ)

Solution steps

\frac{d}{d θ} (sec (θ) tan (θ))

Apply the Product Rule:

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

f = sec (θ), g = tan (θ)

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

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

\frac{d}{d θ} (tan (θ)) = sec^{2} (θ)

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

Simplify

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

= - sec (θ) + 2 sec^{3} (θ)

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