What is the d/(dθ)(r(θ)cos(θ)) ?

The d/(dθ)(r(θ)cos(θ)) is cos(θ) d/(dθ)({r}(θ))-sin(θ){r}(θ)

What is the first d/(dθ)(r(θ)cos(θ)) ?

The first d/(dθ)(r(θ)cos(θ)) is cos(θ) d/(dθ)({r}(θ))-sin(θ){r}(θ)

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\frac{d}{d θ} (r (θ) cos (θ))

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

Solution steps

\frac{d}{d θ} (r (θ) cos (θ))

Apply the Product Rule:

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

f = r (θ), g = cos (θ)

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

Simplify

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

What is the d/(dθ)(r(θ)cos(θ)) ?
The d/(dθ)(r(θ)cos(θ)) is cos(θ) d/(dθ)({r}(θ))-sin(θ){r}(θ)
What is the first d/(dθ)(r(θ)cos(θ)) ?
The first d/(dθ)(r(θ)cos(θ)) is cos(θ) d/(dθ)({r}(θ))-sin(θ){r}(θ)