What is the derivative of f(θ)=θsin(θ) ?

The derivative of f(θ)=θsin(θ) is sin(θ)+θcos(θ)

What is the first derivative of f(θ)=θsin(θ) ?

The first derivative of f(θ)=θsin(θ) is sin(θ)+θcos(θ)

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derivative of

f (θ) = θ sin (θ)

sin (θ) + θ cos (θ)

Solution steps

\frac{d}{d θ} (θ sin (θ))

Apply the Product Rule:

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

f = θ, g = sin (θ)

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

\frac{d θ}{d θ} = 1

\frac{d}{d θ} (sin (θ)) = cos (θ)

= 1 \cdot sin (θ) + cos (θ) θ

Simplify

= sin (θ) + θ cos (θ)

What is the derivative of f(θ)=θsin(θ) ?
The derivative of f(θ)=θsin(θ) is sin(θ)+θcos(θ)
What is the first derivative of f(θ)=θsin(θ) ?
The first derivative of f(θ)=θsin(θ) is sin(θ)+θcos(θ)