What is (\partial)/(\partial θ)(r(θ)sin(θ)) ?

The answer to (\partial)/(\partial θ)(r(θ)sin(θ)) is r(sin(θ)+θcos(θ))

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(\partial)/(\partial θ)(r(θ)sin(θ))

\frac{\partial}{\partial θ} (r (θ) sin (θ))

r (sin (θ) + θ cos (θ))

Solution steps

\frac{\partial}{\partial θ} (r (θ) sin (θ))

Treat

r

as a constant

Take the constant out:

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

= r \frac{\partial}{\partial θ} (θ sin (θ))

Apply the Product Rule:

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

f = θ, g = sin (θ)

= r (\frac{\partial}{\partial θ} (θ) sin (θ) + \frac{\partial}{\partial θ} (sin (θ)) θ)

\frac{\partial}{\partial θ} (θ) = 1

\frac{\partial}{\partial θ} (sin (θ)) = cos (θ)

= r (1 \cdot sin (θ) + cos (θ) θ)

Simplify

= r (sin (θ) + θ cos (θ))

y = x - x^{3}

y \to 0 lim (\frac{y}{sin ( 5 y )})

x \to 2 lim (x - 4)

e^{x - 2}

\int \frac{2 x + 1}{x ^{2} + x} d x

What is (\partial)/(\partial θ)(r(θ)sin(θ)) ?
The answer to (\partial)/(\partial θ)(r(θ)sin(θ)) is r(sin(θ)+θcos(θ))