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

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

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

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

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derivative of

sec (θ) (θ - tan (θ))

θ sec (θ) tan (θ) - 2 tan^{2} (θ) sec (θ)

Solution steps

\frac{d}{d θ} (sec (θ) (θ - tan (θ)))

Apply the Product Rule:

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

f = sec (θ), g = θ - tan (θ)

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

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

\frac{d}{d θ} (θ - tan (θ)) = - tan^{2} (θ)

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

Simplify

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

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

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