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

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

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

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

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derivative of

tan (θ) sec (θ)

- sec (θ) + 2 sec^{3} (θ)

Solution steps

\frac{d}{d θ} (tan (θ) sec (θ))

Apply the Product Rule:

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

f = tan (θ), g = sec (θ)

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

\frac{d}{d θ} (tan (θ)) = sec^{2} (θ)

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

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

Simplify

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

= - sec (θ) + 2 sec^{3} (θ)

\int \frac{\frac{d y}{1}}{y} d x

f (x) = \frac{x}{x - 1}, at x = 2

\frac{d}{d x} ((x + 1)^{5})

\frac{d}{d x} (\frac{2}{5} x^{10})

t^{3} sin (t)

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