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Popular >

d/(dθ)(cos(2θ)cos(θ))

Solution

\frac{d}{d θ} (cos (2 θ) cos (θ))

Solution

- 2 sin (2 θ) cos (θ) - sin (θ) cos (2 θ)

Solution steps

\frac{d}{d θ} (cos (2 θ) cos (θ))

Apply the Product Rule:

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

f = cos (2 θ), g = cos (θ)

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

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

Simplify

= - 2 sin (2 θ) cos (θ) - sin (θ) cos (2 θ)

Graph

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Frequently Asked Questions (FAQ)

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