What is the derivative of (4+sec(θ))sin(θ) ?

The derivative of (4+sec(θ))sin(θ) is cos(θ)(4+sec(θ))+tan^2(θ)

What is the first derivative of (4+sec(θ))sin(θ) ?

The first derivative of (4+sec(θ))sin(θ) is cos(θ)(4+sec(θ))+tan^2(θ)

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derivative of

(4 + sec (θ)) sin (θ)

cos (θ) (4 + sec (θ)) + tan^{2} (θ)

Solution steps

\frac{d}{d θ} ((4 + sec (θ)) sin (θ))

Apply the Product Rule:

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

f = 4 + sec (θ), g = sin (θ)

= \frac{d}{d θ} (4 + sec (θ)) sin (θ) + \frac{d}{d θ} (sin (θ)) (4 + sec (θ))

\frac{d}{d θ} (4 + sec (θ)) = sec (θ) tan (θ)

\frac{d}{d θ} (sin (θ)) = cos (θ)

= sec (θ) tan (θ) sin (θ) + cos (θ) (4 + sec (θ))

Simplify

sec (θ) tan (θ) sin (θ) + cos (θ) (4 + sec (θ)) : cos (θ) (4 + sec (θ)) + tan^{2} (θ)

= cos (θ) (4 + sec (θ)) + tan^{2} (θ)

What is the derivative of (4+sec(θ))sin(θ) ?
The derivative of (4+sec(θ))sin(θ) is cos(θ)(4+sec(θ))+tan^2(θ)
What is the first derivative of (4+sec(θ))sin(θ) ?
The first derivative of (4+sec(θ))sin(θ) is cos(θ)(4+sec(θ))+tan^2(θ)