What is the d/(dθ)(sec(θ)tan(θ)) ?

The d/(dθ)(sec(θ)tan(θ)) is -sec(θ)+2sec^3(θ)

What is the first d/(dθ)(sec(θ)tan(θ)) ?

The first d/(dθ)(sec(θ)tan(θ)) is -sec(θ)+2sec^3(θ)

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\frac{d}{d θ} (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)

\frac{3}{s - 9}

\frac{d}{d x} (f (x) g (x))

\frac{y}{y + \frac{a}{y}}

n = 0 \sum \infty \frac{n}{e ^{2 n}}

\int \frac{e ^{4 x} - e ^{2 x} + 1}{e ^{x}} d x

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