What is the derivative of sin(θ)+θcos(θ) ?

The derivative of sin(θ)+θcos(θ) is 2cos(θ)-θsin(θ)

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

The first derivative of sin(θ)+θcos(θ) is 2cos(θ)-θsin(θ)

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derivative of

sin (θ) + θ cos (θ)

2 cos (θ) - θ sin (θ)

Solution steps

\frac{d}{d θ} (sin (θ) + θ cos (θ))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d θ} (sin (θ)) + \frac{d}{d θ} (θ cos (θ))

\frac{d}{d θ} (sin (θ)) = cos (θ)

\frac{d}{d θ} (θ cos (θ)) = cos (θ) - θ sin (θ)

= cos (θ) + cos (θ) - θ sin (θ)

Simplify

= 2 cos (θ) - θ sin (θ)

What is the derivative of sin(θ)+θcos(θ) ?
The derivative of sin(θ)+θcos(θ) is 2cos(θ)-θsin(θ)
What is the first derivative of sin(θ)+θcos(θ) ?
The first derivative of sin(θ)+θcos(θ) is 2cos(θ)-θsin(θ)