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

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

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

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

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derivative of

θ cos (θ) + sin (θ)

- θ sin (θ) + 2 cos (θ)

Solution steps

\frac{d}{d θ} (θ cos (θ) + sin (θ))

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d θ} (sin (θ)) = cos (θ)

= cos (θ) - θ sin (θ) + cos (θ)

Simplify

= - θ sin (θ) + 2 cos (θ)

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