What is the derivative of d/(dθ)(sin(θ)cos(θ)) ?

The derivative of d/(dθ)(sin(θ)cos(θ)) is cos(2θ)

What is the first derivative of d/(dθ)(sin(θ)cos(θ)) ?

The first derivative of d/(dθ)(sin(θ)cos(θ)) is cos(2θ)

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derivative

cos (2 θ)

Solution steps

\frac{d}{d θ} (sin (θ) cos (θ))

Apply the Product Rule:

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

f = sin (θ), g = cos (θ)

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

\frac{d}{d θ} (sin (θ)) = cos (θ)

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= cos (θ) cos (θ) + (- sin (θ)) sin (θ)

Simplify

cos (θ) cos (θ) + (- sin (θ)) sin (θ) : cos (2 θ)

= cos (2 θ)

What is the derivative of d/(dθ)(sin(θ)cos(θ)) ?
The derivative of d/(dθ)(sin(θ)cos(θ)) is cos(2θ)
What is the first derivative of d/(dθ)(sin(θ)cos(θ)) ?
The first derivative of d/(dθ)(sin(θ)cos(θ)) is cos(2θ)