What is (\partial)/(\partial θ)(r(θ)cos^2(θ)) ?

The answer to (\partial)/(\partial θ)(r(θ)cos^2(θ)) is r(cos^2(θ)-θsin(2θ))

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(\partial)/(\partial θ)(r(θ)cos^2(θ))

\frac{\partial}{\partial θ} (r (θ) cos^{2} (θ))

r (cos^{2} (θ) - θ sin (2 θ))

Solution steps

\frac{\partial}{\partial θ} (r (θ) cos^{2} (θ))

Treat

r

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= r \frac{\partial}{\partial θ} (θ cos^{2} (θ))

Apply the Product Rule:

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

f = θ, g = cos^{2} (θ)

= r (\frac{\partial}{\partial θ} (θ) cos^{2} (θ) + \frac{\partial}{\partial θ} (cos^{2} (θ)) θ)

\frac{\partial}{\partial θ} (θ) = 1

\frac{\partial}{\partial θ} (cos^{2} (θ)) = - 2 cos (θ) sin (θ)

= r (1 \cdot cos^{2} (θ) + (- 2 cos (θ) sin (θ)) θ)

Simplify

r (1 \cdot cos^{2} (θ) + (- 2 cos (θ) sin (θ)) θ) : r (cos^{2} (θ) - θ sin (2 θ))

= r (cos^{2} (θ) - θ sin (2 θ))

\frac{d}{d x} (4 x^{2} - sin (x))

\frac{d}{d x} (A x e^{- 3 x})

\int \frac{csc ( θ ) cot ( θ )}{5 - 4 csc ( θ )} d θ

f (x) = e^{6 x}

(x + 2) d t = 2 t + 3 d x

What is (\partial)/(\partial θ)(r(θ)cos^2(θ)) ?
The answer to (\partial)/(\partial θ)(r(θ)cos^2(θ)) is r(cos^2(θ)-θsin(2θ))