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

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

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

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

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derivative of

θ cos (θ) sin (θ)

cos (θ) sin (θ) + θ cos (2 θ)

Solution steps

\frac{d}{d θ} (θ cos (θ) sin (θ))

Apply the Product Rule:

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

f = θ, g = cos (θ) sin (θ)

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

\frac{d θ}{d θ} = 1

\frac{d}{d θ} (cos (θ) sin (θ)) = cos (2 θ)

= 1 \cdot cos (θ) sin (θ) + cos (2 θ) θ

Simplify

= cos (θ) sin (θ) + θ cos (2 θ)

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